Note: This challenge is now finished and can no longer be completed.
If you already destroyed 50 enemy tanks on the 360, the challenge will unlock upon starting the game. (Accept a few things and then achievements and this challenge will pop) If you're new to World of Tanks, simply start playing. Apparantly only multiplayer kills count. (thanks to Xtowers) If you die, don't wait, but start a new game with another tank.
Tip for getting as many kills in a match: Let other teammates go in first and "snipe" enemies.