You can cheese the T-Rex. Stand behind the trees on the left of the two spike things, so the T-Rex can't touch you. Keep aiming and shooting for around 5 to 6 minutes and it's done. It took me 5:40 to be precise.
See this video:
It may be not the most fun way, but it's the easiest I think. And don't forget to press the right buttons (B and RT) in the following cut scene.