I’m in the same boat as you, trying to make myself as competitive as possible to get into a psych PhD program (though I’ll probably do a master’s first, which will give me more time), so I’ll share some things I’ve learned.
First of all, like I said, you might want to consider a master’s. It does make you more competitive for a PhD program on its face, but considering it gives you more time to accumulate research experience, internships, develop your research proposal (big part for me; I’m hoping to do a psychiatric epidemiology master’s program, and I feel it would be a great opportunity to get started on/develop my research proposal), its benefit extends beyond simply holding a master’s degree. Especially if your gpa isn’t quite where you want it to be yet, it can be a sort of stepping stone school to get into an even better school/program.
Another thing I’m getting started on is learning to program. Graduate schools and PhD programs love students who can code because so often it can be of benefit in a research setting. The more languages you know (and the relevant languages) and the more proficient you are the better. Even better, if you know a certain professor in a program works with certain languages, and you go out of your way to learn them, that will look great.
Pretty much everything else is covered by Juillet I believe. Most important things are research experience, gpa, and relevant courses, as well as the institution you’re doing this at. If you’re at a sort of meh school, you’re almost definitely not going to get into one of the top programs, even if you got a 4.0 and have great experience (there are of course exceptions, like if you truly set yourself apart in your level/type of experience). With that said, you could go from a meh school for your bachelors, to a very good school to get your master’s, to a top-tier school for your PhD.
Extra math skills never hurt, especially for a research scientist, stats especially. Writing skills are fantastic too, and can really set you apart. It’s amazing how many people are terrible writers. Researchers need to be able to write coherently and clearly, and extremely well-crafted essays/statements of purpose can take you to the next level. And you’re definitely going to want to figure out what area you want to do research in well before you starting applying to schools. Just keep narrowing it down, even if you aren’t totally sure yet. Don’t waste a class on something you know you don’t want to do research in just to get your bachelors.