Doesn't have to be confirmed by the Russians. The Ukrainians are certainly recording the planes they shoot down. They have no reason to keep those records secrets, and every reason to publicize them. Currently the (edit: independently confirmed) total number of Russian planes shot down is in the 20s, and probably as many helicopters.
Edit: Apparently Ukraine's military claims they've shot down 189 planes, which seems like a very high number, and orders of magnitude above the independently confirmed numbers. They also claim to have destroyed 986 tanks. Or at least, that's what the sources I can find claim the military claims.