Achievements shouldn't encourage you to be bad or annoying in the game.
I think the idea is good, it's just how it would be handled - a server mod would allow for proper detection of achievements but would only work in achievement-enabled servers and a clientside mod could be cheated upon. A mod that connects to some sort of database online would be possible but it'd have to trust server owners not to abuse it or edit the code...
Random deathmatch-related achievements:
Weapon of Last Resort: With a Hammer as your only tool, kill an opponent which has any other weapon
Indirect Fire: Kill an opponent using another player's Activate event button
Animal Cruelty: Kill a Horse and its most recent rider in the same life
Barely Survived: Survive the blast from a Rocket, Gravity Rocket or Tank Shell (including impact damage from the impulse)
Shockwave: Kill an opponent using the impact impulse from any weapon (including wall slam damage and falling damage)
While He's Down: Kill an opponent who has crashed on the Skis (during or immediately after Tumble)
Think Fast: Kill an opponent during your invulnerability period on spawning
Goliath: Be the sole attacker of and defeat an opponent who has at least twice your scale
Battering Ram: Run over an opponent using a Tank that has had the turret blown up or removed
Big Entrance: Use the Rocket Launcher to remove a wall or Door, and then kill a player on the other side of it using any weapon
Mid-Air Combat
Mid-Air Kill: Score a Mid-Air Kill with any weapon
Unsure of a name: Score a Mid-Air Kill with a Rocket, Gravity Rocket or Tank Shell
Flak Cannon: Kill a flying vehicle while it is in the air while you are on the ground
Tail Gunner: While a passenger in a flying vehicle, kill an opponent in another
Add-Ons
Locksmith: Create ten restricted Doors
Black Hole: Have five players die within one second of being teleported by you (e.g. Portal Gun crush, setPlayerTransform on your brick and then shot)
Emergency Incinerator: Destroy the Weighted Companion Cube through weapons fire