Tyrannosaurus rex is first unlocked when you arrive on Isla Tacaño and its fossils can be excavated from the Frenchman Formation, Hell Creek Formation, and Lance Formation.
By the time you get to Tacaño you'll be familiar with the genome mechanics in the game, once you have at least 50% of the Tyrannosaurus rex genome sequenced you can incubate one in your Hammond Creation Lab and once the Tyrannosaurus rex is released the achievement will unlock.
Getting the T-Rex genome to 100% is one of the requirements for unlocking the Indominus Rex, and there is an achievement for photographing an Indominus rex fighting a T-rex so it's worth getting the genome to 100%.