All of them:
Medal of Prejudice: 100% kills
UAC Star: Get lots of kills. You can't get gold without playing N! or Ao100.
Minor Icarus Cross: Win fast, it seems to imply. I know Kornel has a very strict idea of what "Fast" is (Most timed challenges are ludicrously difficult) so I don't have the major cross.
Gambler's Shield: Pull A LOT OF LEVERS. Seriously, you need to pull almost every one that spawns.
Aurora Medallion: Get lots of uniques. 3 or more, I believe.
Explorer/Conqueror: Win a game visiting/clearing all red stairs.
Compet-n Silver Cross: Get lots of level clears (You feel relatively safe). Gold and platinum are impossible on non-Ao100.
Secret Medals:
Sunrise Iron Fist: Punch the cyberdemon to death.
Malicious Knives Cross: Knife the cyberdemon to death.
Hell Champion Medal: Defeat the final wave of the arena.
Grim Reaper's Badge: Clear the mort!
I DONT HAVE
Dervis' Medallion: Win Ao100 N!
????????: Kill the cyberdemon with the dragonslayer! (I DIDN'T GET IT BECAUSE I WAS PLAYING Ao100 WAAAAAAH)
????????: Kill the cyberdemon with the GCB.