I didn't read through all these, so i hope i'm not duplicating too many. Also note that i haven't played much multiplayer recently, so my memory may fail me, and so some of these medals may already exist.
"assisted suicide" - damage a player shortly before they kill themselves.
"Long throw" or "hail marry" - kill an enemy with a grenade, long after it's been thrown.
"Long shot" - kill from far away. Possible alternatives for projectile, hitscan, and explosive weapons. Example: "Send it" for killing an enemy with a rocket launcher from across a large distance.
"Drop bear" or "Death from Above" - kill an enemy with a melee/assassination after free falling x distance/time.
"Betrayal spree" - lol, no.
"Yoink spree" - lol, yes.
"Mission assurance" - stick a player that was already stuck.
"Sparta" - push an enemy player to their death, with gravity weapons, explosives, or melee (if that becomes a thing).
"Aerial splatter" - to separate from normal ground splatter.
"Marathon" - Run x distance with flag/bomb.
"Close call" - kill enemy while your shields are down.
"Airborne (splatter)" - splatter an enemy with a ground vehicle (or just a warthog) after being airborne for 5 seconds.
"Good catch" - catch a flag/bomb after it's been dropped and is in the air for x distance/time. This would be especially useful if flags/bombs can take gravity lifts.
"Lightspeed" - kill an enemy who is charging up a spartan laser.
"Domino" - kill an enemy with the environment. Example: splatter a player by launching a box at them with a gravity hammer. Alternatively, a nod to the community by calling it "Jenga".
"Samurai" - kill an enemy with a sword after parrying with that enemy at least once.
"Collateral" - kill an enemy by sticking his/her teammate.
"Collateral 2" - kill two enemies with one bullet.
"Calculated" - get a bulltrue with a spartan laser.
"Classic" - kill an enemy while ceremonially crouching on his teammate's dead body.
"Kill Confirmed" - ceremonially crouch on an enemy's dead body.
"Overkill" - stick an enemy (or use a power weapon on an enemy) who has one bar of health and no shields.
"Ball" - stick an enemy player in the head.
"Bounce" - kill an enemy by bouncing a frag off another enemy.
"Power splatter" - splatter an enemy while power sliding a warthog.
"Ghost splatter" - splatter an enemy with a vehicle after jumping out of said vehicle.
"Ghost assassination" - assassinate an enemy while cloaked.
"Chain reaction" - kill an enemy by blowing up a fusion coil with an explosive.
"Ram" - destroy an enemy vehicle by ramming it with your vehicle.
"Reconned" - kill an enemy by splattering them (gravity hammer, explosive, etc) specifically with a traffic cone.
"Unicorn" - headshot kill with needle rifle.
"Direct Hit" - get a kill with a direct hit with a rocket launcher.
"Last Shot" - get kill with last bullet in mag.
More "X sprees" for guns other than shotty, sniper, etc.
"Infected" - infect a player during infection (if that doesn't already exist). In fact, if they don't already exist, all objective-based gamemodes should have something like this (flag/bomb pickup/capture/plant, KOTH stuff, etc.).
"Sacrifice" - get an assist from beyond the grave.
"Stampede" - get a splatter with an elephant.
"Surprise" - get a melee kill without ever appearing on the enemy's radar.
"Skyjack" - highjack an air vehicle.
"Brawl" - melee kill an enemy who has melee'd you.
"Trade" or "lag" - two players kill each other at the same time.
"Noob" - noob combo (plasma pistol charge + magnum headshot) an enemy player.
"Team wipe" - kill every player on the enemy team, so that they are all dead at the same time.
"Final kill" - get last kill of match
"Ender" - Score final point
"Top frag" - earn most kills in a match
"Top talent" - earn highest score in a match
"Bear hug" - while stuck, run close enough to an enemy, so that they are killed by their own team's grenade.
"Eyes closed" - kill an enemy while your game is paused.
"Deflection" - kill an enemy by deflecting a projectile/grenade back at them with the gravity hammer.
"Slap" - Kill an enemy using an objective item (flag/bomb/skull).
"Wrecked" - Destroy an enemy vehicle. Is this not in the game?
"Jun'd" - pop four heads with one sniper mag.
"Spotted" - kill a cloaked enemy player.
"The claw" or "long claw" - kill an enemy by hitting them directly with a grappling hook. I hear a rumor that they'd be in the game.
Note that some of these could be achievements, just as easily as they could be medals.