Ok after trying a few time and not getting this achievement to pop, I decided to look it up on YouTube.
I never saw a timer come up after getting hit by the T.Rex, or an animation from the T.Rex.
He or she will puts his or her head down and charge at the Jeep, you can click down the left joy stick
to honk your horn to get its attention if it helps. Get in some what close to the dinosaur and it will attack.
You can only survive one hit from the T.Rex so once hit you can exist the enclosures and the achievement will pop after 3 minutes has elapsed, again there is no actual timer displayed on screen, now this is the important part I loaded ( ISLA NUBLAR MANAGEMENT ).
This the island where you fist get to build the ( AVIARY ).
From your main menu go to load and then you will see the options for.
Choose JURASSIC PARK.
Good luck guys.