user4748: I'm a graduate student studying plant-insect interactions. My research, necessary for my degree, requires me to collect (kill) a few hundred insects. Are there any suttas, or general Buddhist recommendations, for how a lay person can best approach this? Are there ways to make up for the bad karma incurred by this action?

user11541: I have seen worst. I have seen people eating animals alive. I have also seen people killing people. Your crime is not too big. You should focus on keeping your heart clean. Keep your conscience clean. If you feel you have done wrong i.e. you have been cruel to insects then ask for forgiveness by practicing non violence for the rest of your life.And promise not to repeat such mistakes. If you feel you have done nothing wrong then ask yourself why it was necessary? How it solved the problems of humanity ?  Keep your conscience clean. If you don't have conscience then you need to develop it by practicing good will and compassion.

user254: This won't be the answer you wanted: but I think it's normal for monks to not kill insects. For example, there are monastic rules against their digging in earth which might contain insects.
These specific (monastic) rules don't apply to lay-people. Perhaps it might be seen as an unfortunate reality that lay-people will kill, to some extent: especially as a side-effect of agriculture.
One way to avoid doing that might be to become a monk yourself.
A way to mitigate bad kamma might be to accumulate merit or good kamma (e.g. via generosity, perhaps towards the sangha or, I don't know, perhaps towards insects).
People have also been mentioning the Lonaphala Sutta (AN 3.99: The Salt Crystal) recently.

user9861: Your best (and only) approach to dealing with karma is to understand the Buddhist psychology of karma. This psychology is based upon the concept of sankhara, a Pali term that can be approximately translated as the English term schema (schemata in plural form). Both concepts are complex and sophisticated psychological constructs. Strictly speaking, sankhara can be viewed is a process or as a set of predispositions.
I will start with the process definition because it is easier to understand. As a process, sankhara is the process of selecting a response or action (that may be a mental action or a bodily action) in response to a perceived situation. This process unfolds in a complex manner under the causal influence of a multitude of factors, such as: 

past beliefs determined by past experience, 
innate forms of intelligence that sort out the possible causes and consequences of perceived events and actions, 
an innate and automatic predisposition that causes us to always select the best action given the circumstances, 
the process of perception that selects certain events to be significant while ignoring others (based upon past experience), and 
our experience of “reality” based upon a great multitude of lifetimes.

No matter who we are or how old we are, this process necessarily involves a great deal of intelligence, most of which is unconscious. In Buddhist psychology, we do not have “free will,” as defined by Christian theology. Instead, our choices are determined by how we have understood our past experience. The only source of freedom is knowledge. The better we understand our situation, the better choices we make. There is no equivalent to the Christian concept of blame in Buddhist psychology.
As a set of predispositions, sankhara consists of the psychological causes of the sankhara process. Needless to say, describing a sankhara as a cause of behaviour is a daunting process that is drastically reduced by referring to some belief or wish that merely helps to identify a very complex set of causes. This abbreviation of the description of the set of causes of an action is the source of very serious misunderstandings of the nature of sankhara. For example, it is a serious blunder to refer to “clinging” as a cause of behaviour. It is also a serious blunder to think that killing an insect somehow automatically has some kind of “negative karmic effect.”
Overall, a great deal of wholesome (kusala) sankhara is acquired by being a “graduate student studying plant-insect interactions,” because a factual and objective understanding of biological processes is very conducive to wholesome behaviour and understanding. But, independently of whether or not you kill any insects, you lack the deep meditative understanding and appreciation of life itself and its many hidden causes. Through no fault of your own, you have no awareness of the deeper dimensions of the mind. This can be acquired only through many years of mindfulness meditation or vipassana.
I wish you well in your practice and suggest that you not be concerned by such a superficial understanding of karma. You cannot “make up for the bad karma incurred by this action” because it does not exist. I suggest you meditate on the complex causes of action and come to appreciate the extraordinary dimensions of human intelligence.

user13443: Don't let the four parts of the karmic path get completed. The four parts are basis, intention, action and completion. In this case, the best way would be to stop at the last step and develop intense regret for the action. However if this is a regular action, the regret will not be genuine. 
The other is to put the four opposite forces into action.
https://learning.tergar.org/wp-content/uploads/2013/05/The-Four-Powers-copy.pdf
This requires you to commit to not doing the karma again, at least for a specific duration of time.
The last way is to do the 35 Buddhas confession practice:
https://www.lamayeshe.com/article/chapter/appendix-3-confession-downfalls-thirty-five-buddhas

user43: How to mitigate the negative karmic effect of killing
Generally speaking it can't be done. 
Don't kill. Tell your teacher you're a Buddhist. 
However, if in this particular case you have made up your mind on killing... At least you can cleanse your own mind. Please perform a Bardo Deliverance ceremony for each insect. Exact details don't matter, what matters is your sincerety, so you can make up the exact ceremony yourself. Should be at least 20 minutes long per insect, first stand on your knees and talk to each insect, explaining why you have to kill it and what benefits it will bring to the world, and asking forgiveness from the insect and the future generations of its children, not to be born because of you. Make it clear that you don't think that you are better or higher than the insect. Then, after you kill it, talk to it again and promise a swift rebirth in a pure land of Tushita, where it can listen to the teachings of Maitreya. Describe what it will look like to live in Tushita heaven and tell the insect how awesome it will be to learn directly from the great Bodhisattva. Make a vow to the world, that through the power of your compassion these promises will actually come true and they will. Say thank you, to each insect individually, for being your teacher at the moment and giving you this lesson on interconnectedness. Have a clear understanding that at that moment the insect is in fact a representative of the Dharmakaya, teaching you. 
If other people happen to see you, don't hide. Explain that you are a Buddhist and relay to them the outlines of the ceremony in broad terms. This should seed enough good seeds to offset the negative effects, in this particular case.
This is an overall scheme. Like I said, what matters is your sincerety. Feel free to improvise and elaborate. 

user111: Wanting to become a degree holder is Bhava-tanha or craving to become. That craving is causing you to break the first precept. See how dependant origination is at play here.
You can either look for insects that are already dead or tell your professor that you cannot kill as a Buddhist. 

4748: <p>I'm a graduate student studying plant-insect interactions. My research, necessary for my degree, requires me to collect (kill) a few hundred insects. Are there any suttas, or general Buddhist recommendations, for how a lay person can best approach this? Are there ways to make up for the bad karma incurred by this action?</p>
 11541: <p>I have seen worst. I have seen people eating animals alive. I have also seen people killing people. Your crime is not too big. You should focus on keeping your heart clean. Keep your conscience clean. If you feel you have done wrong i.e. you have been cruel to insects then ask for forgiveness by practicing non violence for the rest of your life.And promise not to repeat such mistakes. If you feel you have done nothing wrong then ask yourself why it was necessary? How it solved the problems of humanity ?  Keep your conscience clean. If you don't have conscience then you need to develop it by practicing good will and compassion.</p>
 254: <p>This won't be the answer you wanted: but I think it's normal for monks to not kill insects. For example, there are monastic rules against their digging in earth which might contain insects.</p>

<p>These specific (monastic) rules don't apply to lay-people. Perhaps it might be seen as an unfortunate reality that lay-people will kill, to some extent: especially as a side-effect of agriculture.</p>

<p>One way to avoid doing that might be to become a monk yourself.</p>

<p>A way to mitigate bad kamma might be to accumulate merit or good kamma (e.g. via generosity, perhaps towards the sangha or, I don't know, perhaps towards insects).</p>

<p>People have also been mentioning the <a href="https://www.accesstoinsight.org/tipitaka/an/an03/an03.099.than.html" rel="nofollow noreferrer">Lonaphala Sutta (AN 3.99: The Salt Crystal)</a> recently.</p>
 9861: <p>Your best (and only) approach to dealing with <em>karma</em> is to understand the Buddhist psychology of <em>karma</em>. This psychology is based upon the concept of <em>sankhara</em>, a Pali term that can be approximately translated as the English term schema (schemata in plural form). Both concepts are complex and sophisticated psychological constructs. Strictly speaking, <em>sankhara</em> can be viewed is a process or as a set of predispositions.</p>

<p>I will start with the process definition because it is easier to understand. <strong>As a process, <em>sankhara</em> is the process of selecting a response or action (that may be a mental action or a bodily action) in response to a perceived situation.</strong> This process unfolds in a complex manner under the causal influence of a multitude of factors, such as: </p>

<ol>
<li>past beliefs determined by past experience, </li>
<li>innate forms of intelligence that sort out the possible causes and consequences of perceived events and actions, </li>
<li>an innate and automatic predisposition that causes us to always select the best action given the circumstances, </li>
<li>the process of perception that selects certain events to be significant while ignoring others (based upon past experience), and </li>
<li>our experience of “reality” based upon a great multitude of lifetimes.</li>
</ol>

<p>No matter who we are or how old we are, this process necessarily involves a great deal of intelligence, most of which is unconscious. In Buddhist psychology, we do not have “free will,” as defined by Christian theology. Instead, our choices are determined by how we have understood our past experience. The only source of freedom is knowledge. The better we understand our situation, the better choices we make. There is no equivalent to the Christian concept of blame in Buddhist psychology.</p>

<p><strong>As a set of predispositions, <em>sankhara</em> consists of the psychological causes of the <em>sankhara</em> process.</strong> Needless to say, describing a <em>sankhara</em> as a cause of behaviour is a daunting process that is drastically reduced by referring to some belief or wish that merely helps to identify a very complex set of causes. This abbreviation of the description of the set of causes of an action is the source of very serious misunderstandings of the nature of <em>sankhara</em>. For example, it is a serious blunder to refer to “clinging” as a cause of behaviour. It is also a serious blunder to think that killing an insect somehow automatically has some kind of “negative karmic effect.”</p>

<p>Overall, a great deal of wholesome (<em>kusala</em>) <em>sankhara</em> is acquired by being a “graduate student studying plant-insect interactions,” because a factual and objective understanding of biological processes is very conducive to wholesome behaviour and understanding. But, independently of whether or not you kill any insects, you lack the deep meditative understanding and appreciation of life itself and its many hidden causes. Through no fault of your own, you have no awareness of the deeper dimensions of the mind. This can be acquired only through many years of mindfulness meditation or <em>vipassana</em>.</p>

<p>I wish you well in your practice and suggest that you not be concerned by such a superficial understanding of <em>karma</em>. You cannot “make up for the bad karma incurred by this action” because it does not exist. I suggest you meditate on the complex causes of action and come to appreciate the extraordinary dimensions of human intelligence.</p>
 13443: <p>Don't let the four parts of the karmic path get completed. The four parts are basis, intention, action and completion. In this case, the best way would be to stop at the last step and develop intense regret for the action. However if this is a regular action, the regret will not be genuine. </p>

<p>The other is to put the four opposite forces into action.</p>

<p><a href="https://learning.tergar.org/wp-content/uploads/2013/05/The-Four-Powers-copy.pdf" rel="nofollow noreferrer">https://learning.tergar.org/wp-content/uploads/2013/05/The-Four-Powers-copy.pdf</a></p>

<p>This requires you to commit to not doing the karma again, at least for a specific duration of time.</p>

<p>The last way is to do the 35 Buddhas confession practice:
<a href="https://www.lamayeshe.com/article/chapter/appendix-3-confession-downfalls-thirty-five-buddhas" rel="nofollow noreferrer">https://www.lamayeshe.com/article/chapter/appendix-3-confession-downfalls-thirty-five-buddhas</a></p>
 43: <h2>How to mitigate the negative karmic effect of killing</h2>

<p>Generally speaking it can't be done. </p>

<p>Don't kill. Tell your teacher you're a Buddhist. </p>

<p>However, if in this particular case you have made up your mind on killing... At least you can cleanse your own mind. Please perform a Bardo Deliverance ceremony for each insect. Exact details don't matter, what matters is your sincerety, so you can make up the exact ceremony yourself. Should be at least 20 minutes long per insect, first stand on your knees and talk to each insect, explaining why you have to kill it and what benefits it will bring to the world, and asking forgiveness from the insect and the future generations of its children, not to be born because of you. Make it clear that you don't think that you are better or higher than the insect. Then, after you kill it, talk to it again and promise a swift rebirth in a pure land of Tushita, where it can listen to the teachings of Maitreya. Describe what it will look like to live in Tushita heaven and tell the insect how awesome it will be to learn directly from the great Bodhisattva. Make a vow to the world, that through the power of your compassion these promises will actually come true and they will. Say thank you, to each insect individually, for being your teacher at the moment and giving you this lesson on interconnectedness. Have a clear understanding that at that moment the insect is in fact a representative of the Dharmakaya, teaching you. </p>

<p>If other people happen to see you, don't hide. Explain that you are a Buddhist and relay to them the outlines of the ceremony in broad terms. This should seed enough good seeds to offset the negative effects, in this particular case.</p>

<p>This is an overall scheme. Like I said, what matters is your sincerety. Feel free to improvise and elaborate. </p>
 111: <p>Wanting to become a degree holder is Bhava-tanha or craving to become. That craving is causing you to break the first precept. See how dependant origination is at play here.</p>

<p>You can either look for insects that are already dead or tell your professor that you cannot kill as a Buddhist. </p>
