I wrote this solution 5 years ago when I wasn't good at combat, but subsequent playing through various Arkham titles has made me a master at combat, so I'm simplifying the solution.This achievement is potentially unobtainable on your save file, if you are unable to unlock Campaign Mission 10, "Darkest Night"
. Please see discussion in the forum Locked Challenge Campaign after completing the majority of game
as well as Solution for Olympian in Batman: Arkham Origins
for more information including advice on how to fix the issue.
Ensure to load the bad handicaps (reduced health, no special combos, no gadgets) in the first challenge. It will make the second and third challenges in the set of 3 a lot easier and there's enough enemies in the first challenge to get 3 medals even when really handicapped. Always use Reduced Health in the Fighting rather than in Predator, as in Predator you get just one bar whereas in Fighting you get about half your usual life but it will refill at the end of each round.
You don't need to be too fancy here except to evade (LT + A A) when you get too surrounded or are facing an enemy you cannot strike directly (e.g. those holding car doors or electrified prods). Also learn to time your counters when being surrounded by simple thugs. If you can keep your combo up you can often surpass the 3 medal requirement very easily: in one situation getting 3 medals required 72000 points, and I just wasn't able to nail this down. Eventually with practice, I kept my combos up very high and ended up getting 125000 points for that fight.