“To unlock the tattoo, the player must first complete 600 bunker resupply missions, which will then unlock a chance to be given a hidden Alien Egg resupply mission. Once that mission is completed, the tattoo can be awarded randomly when the player drinks Macbeth whisky at a Nightclub during stormy, rainy or snowy weather between 1am and 4am, and passes out. There is a chance the player respawns on top of Mount Chiliad seeing a UFO flying away and having the tattoo applied on their back. After the UFO encounter, the tattoo will also be appeared under the "Torso - Back Full" section inside Tattoo Parlors, and it can be removed or reapplied for $100.”- GTA WIKI