It used to be a score of 40+ out of a 45 HPS on the APWT (the annual MATT shooting test). Since that has now changed to the ACMT the score may be different, but the answer will still be in the PAM, which you can get by asking the SAA wing at Sandbags.
As crow_bag points out, plenty of senior term cadets, about 30% from my rough estimate, get marksmanship badges because RMAS does (or at least did, I may be out of date) the non-combat arms version, and not the infantry version which extends the shoots out to 400m and is somewhat harder.
When I worked at ITC(C) we used to issue the Marksman badges to the rcts when they earned it, but because they only wore their No2 dress for four hours, there was little point sewing the badges on. Arriving at Bn with it on the badge would have been unecesary drama for a rct.
The re-introduction of marksman badges at RMAS was a really good move IMO. There were a few snipers who came through as OCdts who drew second glances, though!
Must be some wonderful dream then when I see them wearing said badges on their blues when they're outside the GD RM on show parades and rehearsing for things like Sovereigns Parade, but what would I know I've only worked there for the last year and a half.
The only real marksman i can remember at Sandhurst was the "Barossa Sniper" who used to shoot the fatties on the Tabs causing them to plunge into a ditch/hole in the road/stream injuring their ankle/knee/spine in the process.