Andrei-- I tend to be a pragmatist about this sort of stuff so many someone else will have better advise for you.
First, if it's slugs, you'd see the slimy trail they leave & I didn't see that in your photos (although I didn't look too carefully). I doubt that it's squirrels. Squirrels tend to eat
flowers & fruits more than leaves, at least this is my experience and I have a ton of squirrels.
Unless the damage is severe, I don't worry about this on my eggplant for two reasons. First, I'm eating the fruit not the leaves! As long as the plants blossom and set fruit, I'm not too concerned with some minor damage. Second, and I say this with some reservation because I don't know if flea beetles are vectors for more serious viral diseases, an otherwise healthy plant can withstand a bit of nibbling. As the plant gets bigger, the damage is proportionately less, unless there's a serious infestation.
I might also add that the new growth looks fine to me. In my experience, eggplant is going to continue to grow & grow. So if you're only seeing damage on the older leaves, and the new growth is not being chewed up, I'd say you're o.k. If you do see damage to new growth, then I'd worry.
Maybe someone else has better thoughts, though. Last year was the first time I grew ewggplant (and I had the same problem).
Good luck!