Your best strategy is to fire as fast as you can, as often as you can, and with the most powerful weapons that you have. You will need the rocket launcher however to finish him off. All this while making sure to keep your distance and avoid him. He walks slow, but has the ability to run at you very quickly and take a giant swipe. Be prepared for this as it is his main form of attack. A single claw strike against your character. This does a small amount of damage depending on which version of the Tyrant your facing.
During the second battle the Tyrant can also make a running slash at you. As shown in the screen this is easy to dodge by running away from the direction he is heading towards. Should he pull out his larger claw and come running for you he can sometimes use it as a backhanded attack and smack you across an area of the heliport. This can be disorientating if you slide backwards over a couple of screen changes.
Again with the second battle, although it does happen a sometimes in the first, should you have enough health and the Tyrant is close instead of using the claw to hit you he will stab at you with it. It does a fair bit of damage though, so check your health and heal if you need it. If your on the end of the skewer I can say your dead. In both battles should you be on danger and the Tyrant attacks, you will be impaled upon his claw. Not the greatest thing to happen. Your fighting tactics should change slightly depending on which encounter your at.
1st Encounter -
Colt Python, Colt Python, Colt Python. Before battling the first form of the Tyrant you need to have the Colt with about a full round (6 shots) of ammo. While he usually only takes 3 shots, depending on the version and how the game feels it may take more than this. You should also have a back up weapon just in case. All you need to do is run and wait on one side of the room and shoot at him as he comes close. Repeat until he is dropped.
2nd Encounter -
Fill all but one slot with herbs. While you probably wont need more than one, if any at all, be prepared. You'll need the other single slot for items. All you need to do here on the heliport once you've lit the flare is run in circles avoiding the Tyrant, until the clock gets around or just under 30 seconds. At this time Brad will drop the rocket launcher. Run in, grab it, line up your shot and fire. If you targeted well enough one shot will be all you need.