This requires a good amount of luck.
First of all, don't equip anything that makes you move after you're dead. You need many attempts to understand how space you take to completely stop after a collision. Try and retry several times, it's just a matter of luck, you eventually get the achievement.
Out of clothing, jetpacks, and vehicle upgrades only the following provide any actual tangible benefit:
Hog Magnet
Stomper Magnet
Teleporter Magnet
Bird Magnet
Gravity Suit Magnet
Mr. Cuddles Magnet (added in the Oct./Nov. 2011 update)
The benefit of any of the Magnet items is that they attract coins that are close by without having to touch them. The clothing and jetpack upgrades provide only an aesthetic benefits, although some of them do help toward gaining certain Achievements.
Best Answer
According to Jetpack Joyride wikia:
This requires a good amount of luck.
First of all, don't equip anything that makes you move after you're dead. You need many attempts to understand how space you take to completely stop after a collision. Try and retry several times, it's just a matter of luck, you eventually get the achievement.