SpiderHeck

This can be done easily in versus mode (you need 2 players/controllers to start a versus match), just set up your lobby with all weapons disabled other than "biggest grenade" then go to modifiers and click Bigger Boom twice so it should say Bigger Boom +, now load into a game and set off one of those bombs for the achievement.

This can also be done in survival by picking up the Bigger Boom perk twice when it shows up, still easy enough but more luck based on whether the perk shows up or not.