Supervisor/advisor ignores me regarding my paper I did an honours degree last year (4 year undergrad study with a research  thesis). My supervisor shafted me towards the end of that year when I was coming up to submit my thesis by being absent with his own life issues and barely communicative, and gave me back drafts literally days before it was due. End result was I fell barely short of the requirements to get a PhD scholarship. So I discussed with my supervisor and he said I could write a paper with his assistance about my work, to bolster a future PhD application.

So we agreed on a date to catch up, the time came and I sent him an email. He has not responded at all, it's been 10 days at this point. Normally he would reply back quickly. I'm getting the strong feeling he's got yet another excuse, but I really need to do this for my professional development/future PhD application. What should I do next? Would it be possible to write the paper myself without assistance (I have all the data).
There are many reasons why people can miss an email; a likely possibility for busy people is that your email simply got buried under many others. So, don't assume he's trying to ignore you, and you should first bug him again (politely) about that.

It is also a good idea to start writing the paper on your own: your supervisor will be much more willing to help you improve a first outline or even a draft than to start from a blank page.