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The Vampire Gun costs $1,430 and can be purchased from the Garage in the Weapons section.
Purchase the Vampire Gun and equip it to one of your slots (up, down, left or right).
I would recommend fully upgrading the Vampire Gun as it is much faster to drain an opponent with an upgraded weapon.
Vampire Gun - $1,430 > $1,430 > $1,560 > $1,690 > $2,600
To get this achievement you should let your opponents group together so you can drain multiple opponents at once. This achievement is cumulative across races.
Please comment if you vote negatively. I will edit my solution to make it better.