Tips for interviewing for promotion within the same company?

Hello! I have the opportunity in a few weeks to interview for a promotion being handled via internal hiring within a company I was at before. I worked for this company with the same supervisor last year for a student contract position in the summer. My prior supervisor will be leading this interview. I am very interested in this position and will of course be preparing as hard as possible as I would for any other job interview - but I'm kind of having trouble understanding how I can really sell myself. My supervisor already knows me - and while I was given a very positive review at the end of my contract last year, there are definitely things that I intend to improve/change this year (some of which that we discussed) that I think would make me a more desirable employee, and I don't know how, or even if, I should bring those up in the interview. I'm not even sure there's any point - I mean who's going to believe someone just \*saying\* that they'll change something without evidence? To be clear, there was nothing major or terrible that I did previously, and I will still have a role with them again this year even if it's not the promotion. For more context, this promotion is still an entry-level role, doesn't pay much more than minimum wage lol. But still, there are greater overall and leadership responsibilities than what I had with them previously. (Kind of irrelevant, but I'm just worried they'll promote someone who was in a lower position than I was despite the months more experience I have with the company, my good performance in the other areas, and the fact that they've done this same promotion move before (from my old position to this other one). And I mean, it's of course totally my fault if I didn't leave a good enough impression last year. I just wish that I'd somehow had a chance to prove myself before interviewing for this next opportunity, and I don't know whether there's any real room in this interview to try and make up for my previous shortcomings.)