Be sure to save before trying, so if you die, just reload the previous save.
Find one of the three spiked logs and stand in front of it. You're going to have to shoot at the T-Rex to fill it's "rage meter." This will cause the T-Rex to run at you, just press B while holding left/right when the screen blurs. Wait for the reticule to join and then you shoot, this causes the T-Rex to run into the spiked logs. Doing this two more times will kill the T-Rex, just make sure to press B, then Right Trigger during the cutscene.
Here is a great video by klioki, for a visual image.