For the Special Edition of Tower of Guns the quickest way to kill yourself is to use the following loadout:
Game Mode: Hotfoot
Perk: Tunnel Rat
Gun: 60MM Hand Cannon
Hotfoot hurts you when you land from a jump so when your temporary invulnerable wears off you just need to jump and land 3 times, this is much faster then shooting the ground with the hand cannon.
You can make it even easier by having the Xbox app on your phone and just tap the jump button every few seconds. I got the achievement notification on my phone while passing time browsing the web on when I got the achievement.
This only works on the Special Edition versions because Hotfoot isn't available on the download version.