Edit: There is no longer a Rumble Pit playlist, but these rules and general strategy still apply. The playlist doesn't really matter, although the principal of more enemies means more kills still applies.
There's a number of ways to do this, and it also depends on how you go about getting these multiplayer achievements.
If you want to boost:
Use the methods in other solutions to get in a game with a boosting lobby. I'd recommend boosting Executions by tossing a few nades in a group of 4, pick up nades from the fresh bodies, and repeat. If everything goes well you'll have around 400 kills once you hit the 100 legendary medals. Simply boost a bit more to mop up.
Figure out how much health you need to throw a nade at someone to kill them. Even a singular perfectly placed grenade can kill a full shield enemy. I'd recommend popping someone at least twice with a BR, Pistol, etc, depending on the game and throwing nades trying to depict their path.
Otherwise, use something called prenading, where you toss nades in popular areas or around corners to at least lower enemy shields.
As always plasmas are your friend as a well aimed throw ends in a stick and guaranteed kill. Also take any advantage in finding an AFK player to kill them for an easy kill.
Lastly, I'd recommend you play Rumble pit. 8 players means lots of grenades from bodies, lots of duels leaving weak players for your picking, and in general more enemies means more targets means more kills. Personally Halo 1 Rumble pit finds me the most success. Simply pop an enemy 1-2 times with a pistol and place a frag near him. Or just stick him. Thankfully you get 4 plasmas in Halo 1 and 2 so you have extra ammo to toss around.
Any feedback or questions let me know. This is a pretty straight forward achievement, just thought I'd add a guide for anyone looking for extra tips. Thanks for reading guys!