To be fair, VANDAM also holds the Sunrise Iron Fist, but that was a very long time ago. Still, his player stats showed he never won, so I figured it was worth a try just playing fists only melee for awhile - and to be fair, as strong as Brute is, and as useful as Finesse is for melee, it's actually not too difficult(though it's certainly more of a challenge then using weapons).
As far as the un-earned medals, the Peace Pin sounds like it's reliant on making monsters kill each other, rather then doing it yourself, but how to actually make that happen is beyond me. The UAC Achievement Medal is fairly low in the hierarchy, so I can't imagine it's all that difficult to acquire, but I don't really have a clue where to begin on that one.
Edit: VANDAM is also the sole holder of the Shadow Cross... my only guess would be that it has something to do with the invisibility powerups? At least with Sunrise Iron Fist I had the DRL version of the medal as a guide.
Edit2: LongDong appears to be the sole holder of the Survivor Ribbon. My only guess on that is it's something like Explorer/Conqueror.