I used to get dry eyes/tons-of-blinking, but I realized it was only because I blinked too much once and then thought it had something to do with osu! and kept thinking about it when I played, so that in turn caused excessive blinking. Once I realized that it pretty much stopped.
Use flux, keep your room lit, sit far from the screen, make sure you're staring directly at it, and stuff like that. osu! is not bad for your eyes, but the screen is.
tbh I've noticed my peripheral vision got a lot better actually, probably because I play on a 1920x1080 resolution. Pretty neat really.