-Use the Stinger missiles and run when it is about to attack.
-Go under Rex; he will not see you; if he does he going to attack you. Toss a chaff grenade anywhere. It is still going to stun for a few seconds. Stand behind Rex and fire a Stinger missile at the radar dome. REpeat this until the radar dome is destroyed. After the FMV sequence, keep firing stinger missiles at the cockpit until he dies.
-You do not need a lock-on to defeat Metal Gear Rex. You can also aim the Stinger at the radar dome (part 1), or the cockpit (part 2), and fire. This works especially well in part 2 by running between his legs and firing at the underside of the cockpit.
-Before he wakes up, go behind him and prepare to shoot. When he moves or turns, shoot him then toss a chaff grenade. Shoot him again until the chaff wears out. Immediately before it wears out, get behind him and kill him.
-Hide behind one of the parts sticking out on either side of the room, then just wait until Rex turns around and shoot him. Hide behind the part sticking out just before the missile hits him. This only works while shooting the round thing on his left arm. Keep doing this and you should be able to defeat him after some time.