Unreal Tournament 3

Host an MP game with the following settings...

Host match>Player match
Deathmatch
Max players 16
private slots 16
Bots: Novice
Map: Rising Sun
Mutators: Weapon replacement - replace everything with Enforcers.

Dual Enforcers cut through bots like hot butter and you don't die NEARLY as much as you do with instagib, rockets, etc....so Monster Kills come very easily. Keep in mind that it only counts ONE per game. You can't get 20 monster kills in one game to unlock the achievement. It reads "Got the "Monster Kill" award in 20 matches."....not "Get 20 Monster Kills".

Additional commenter tips:

Voldrox: i chose the same settings only change the map to morbias arena and enabled speed freak in the mutators monster kills came very easy this way

Whiteboy504: my favorite way to get an monster kill is to do CTF on Facing worlds with 16 bots. Sit on the very top of the tower with the sniper (sit on an ammo crate to reload) and you can get a monster pretty easy. But that's probably not the most efficient/easy way to do it...

HaloHore2000: doing the same in Capture the Flag on Hydrosis works well too (I did it on instant action though).

Here is a much easier way.

Host Match > Player Match
CTF on Facing Worlds.
Max players 3.
Private Slots max.
Player to Bot Ratio 1:2.
Bots Novice.
Mutators: Weapon replacement with whatever you like most (I recommend Link Gun because it's quite fast.)
Caps can be set to whatever, but I recommend 1 so you can cap once to end the game.

When the game starts, collect ammo until you are maxed out. Get the super health pickup and the enemy flag. Get your flag back if it's been taken, then run behind the enemy base (where the enemy bots spawn). The bots will follow you back here. Kill them, and they will keep respawning in the same 2 spots over and over so you can keep drilling them and EASILY get a monster kill and you don't even have to move. Once you have your MK, return the flag, restart the game, and repeat 19 more times.

Here's a video I made
I hope it helps ^^ I personally prefer Visual Aid
If you vote down please say why so I can fix the solution
Thank You and Have a nice day :)