BattleBlock Theater

i found the easiest way to do this is story mode (although arena kills do count)

go in a local co-op with a second controller, choose one of the first levels and stand next to a flagpole.

now you can use your weapons (working on the achievement for using all weapons) or just shove them into water or spikes for this kill to count.

your teammate will spawn right next to you so you can quickly kill him again. also doing this in story mode gives you no time limit (unlike arena), so you can quickly get this in one sitting.

Edit: WolfheartSpell said that these kills also count for the 100 kills achievement

Note: You will need a second controller to use this guide!

There is a simple way to do this before even entering the first level. With two controllers active, start a Local Co-op/Story game (I chose Normal mode), and choose your characters.

When the cutscene begins, wait a few moments and skip it by pressing START. Move both characters forward, down the steps ahead of your starting position. Hold Y next to your opponent (controller 2) to "suicide," causing him to explode. Repeat 49 times and you'll have your achievement in no time!

You can check your kill count by pressing START, scrolling right to "Player Stats," and pressing A twice to view your stats.

You can do this in any mode with 2 controllers or online with your friend, when starting the game select the grenade and throw it until the achievement unlocks, you must unlock this achievement throughout the game by accident.