I'll assume you're mainly interested in tech skills. Soft skills obviously aren't specific to AI, although as the other commenters humorously point out, there are certainly differences between startups and big companies that you'll want to understand. One in particular is basically being comfortable with uncertainty and understanding how to navigate it. Good communication and emotional self-management are key here.

As far as tech skills, there isn't a one size fits all answer -- the landscape, even within "early-stage startups in the AI space", is simply too broad.

You can get a good idea of what tools are most commonly used in the area just by browsing the web, looking at blog posts and open source projects, etc.

More specifically, I recommend going to LinkedIn or whatever job posting site you prefer and finding a bunch (10-20?) job postings that really excite you and tallying up the most commonly required skills. Go learn those, build up a portfolio of online demos and git repos, and you'll probably be as prepared as you can be to navigate the job market.