Relevant experience but I did a mediocre job.. should I include it in the cover letter? I am writing a cover letter to apply for a paid PhD position. I was thinking if I should include the experience of doing my master's dissertation. The methodology is very similar to that of the project, but the problem is I did a mediocre job in the dissertation (got a C, meaning "Good"). I am ashamed by the grade and was thinking for this highly competitive position, a "good" job might be kind of bad.. Should I include it in the cover letter or just leave it and highlight my other experiences (which are not quite research-related)?
This may depend somewhat on your country and your discipline, but in general a PhD is a research degree.  Research experience is the absolute most important and relevant experience.  Any research experience at all is better than none. You should mention it.