When you start this, you should be around a campfire with Hayes and Carl. Follow them out to the bridge, where you will see your fellow comrads. Unfortunately, your reunion will be ruined by the T-Rex as he eats one of your friends. When he roars at you, turn around and run through the pillars. Hayes will tell you to distract the Rex while he opens the door. Normally, you can just shoot him to get his attention, but who wants to risk their own life? While messing around, I found that you can actually take control of one of the turning pillars by walking up to Hayes and pressing R. He'll step off and take his defensive position against the T-Rex. You can continue to open the door as Hayes holds him off, however, the Rex DOES still have a chance of eating him, so you have to be careful. Once the door is open, run through and run all the way to the pillars and hide behind them. If you hide back all the way in the water, the Rex won't see you, but he'll try to smell you. Eventually, he'll just pass. There you have it! A way to beat the Rex without using any ammo!