NeuroVoider

Play through the game until you get a special level and hope it's an auto-destruct level. I've only gotten two of these so far. It's completely random which special level you get but there seems to be one between each boss battle. An auto-destruct level gives you a timer, and you must complete the level before the timer reaches 0. I've never failed one of these, but I would assume you die and get a game over if the timer reaches 0. Don't mess around too much and just focus on completing the level, and the achievement is yours.

I like using Fortress with the Self-Repair skill. Then fully upgraded dual rockets to blast my way through everything. This may not be the way to go for this achievement, but it's what I got used to.