Hartmann had the highest score. Yes. 352?
He had the USSR to deal with mostly. And for a lot of time inferior aircraft with inferior tactics. He did get shot down, and actually had both crashed an aircraft as well as chased his own wingman before he set the beads on a russian fighter.
Barkhorn was another, a crack ace. 302 kills?
Then Rall, 275. He got shot down 8 times. However, he bagged an aircraft in his first operational sortie and went on ops on many theaters, - France, BoB (which he considered very dangerous air-to-air), Crete, Romania, USSR ,then the western front again (Which he considered to be a very deadly environment). Considered the LW's best shot together with Marseille. Rall poo's on USSR claims by the way. (When the commisar demands results he will get results. On paper if necessary

).
One of my favourite ace is "Pat" Pattle, since he had hard dealings and bagged 15 aircraft in a bipe. And one of the best of all was perhap's the S-African "Sailor" Malan, who reduced his score by sending LW bombers home alive but bleeding, - as a warning.
Malan also clobbered one of the German Aces, Werner Mölders (The top LW gun at the time) in a dogfight where Mölders started off with the advantage. Malan's excentrism with "bleeding enemies" perhaps saved Mölders?
AFAIK the LW claims were however quite authentic. Not in the BoB (But neither were the RAF's), but after. I have only found a couple of incidents (I scanned 1942, ETO) where the LW claimed above the RAF's losses, but not much. However in the Med, Russia and generally in big action, claims can get tricky to confirm. Isn't Marseille's day with 17 kills still disputed?
(AFAIK JUST his claim exceeds RAF and SAAF losses, let alone the AC types claimed)
that's....war....