The best way to overcome the giant electronic bird is to find a relatively safe spot, preferably near to where you picked up the Talion artifact. There are a few alternative methods to killing him. Depending on which path you wish to take, refer to the desired method.

After collecting the Talion artifact from the room with the broken ice windows, head through the window which faces the door to the third secret. As soon as you hit the ground and walk towards the arena, the big scary thing will reveal itself.

As the Guardian makes its way towards you, a good place to stand is on the raised block, outlined in red in the following screenshot.

Standing here will prevent him from being able to reach you, and will anger him, as shown in the example below.

This gives you the opportunity to strike. Equip the weapon of your choice, preferably the M16 or Grenade launcher. Pull off as many shots as possible until he cowers. When he runs out of your shooting range, jump to the ground. This will attract him, and he'll start thumping towards you again. As soon as he's close enough to you (make sure you're out of his attack range), backflip back onto the block and open fire. Shoot him for as long as possible until he cowers again. Repeat until he dies.

Another good place to stand is on the block on the other side of the ice window room, shown in the screenshot below.

You can use the same strategy here, shooting the Guardian for as long as possible until he cowers, then jumping down to the "X" marked in the screenshot, and backflipping back up to the ledge. There is not much of a difference, so either way, as long as you are positioned correctly, you should be able to defeat him with ease.

If you want the two pick-ups in the Guardian's cave, you will need to lure the Guardian as far away from that cave as possible, preferably towards the ladder in the far left corner. The depression in the ground is another spot where the Guardian can't hurt you, as shown here...

When he approaches you, jump out of the depression to the left. Run and jump around the outside of the arena as fast as possible, around the columns, and into the cave to collect one of the two items. Once picked up, the Guardian should be just entering the cave upon your exit. You should have enough time to escape, make your way back towards the depression near the ladder, and repeat the process to retrieve the second item. After that, you may proceed to killing him.

There are many different ways to defeat the last boss of the game. The most effective, and safest way to do this is to use the pillars for cover from his fiery breath, with the Grenade Launcher as your primary weapon. The Uzis are preferrable if you wish to charge into a head-to-head battle. Be aware that the main objective is to first bring the dragon down, then rush to its belly as quickly as possible, and pull the dagger from his heart.

After using the Mystic Plaque to enter the Dragon's Lair, slide down the slope and continue forward towards the body lying in the middle of the arena. Before advancing past the pillars, equip the weapon of your choice. As I said before, the Grenade Launcher will prove favourable when occasionally using the pillars for cover. The use of the Uzis in a head-to-head battle is also an option.

As soon as your weapon is equipped, and your strategy is decided, prepare to fight the final boss of the game. Advance past the pillars, and the body lying in the middle will begin to transform. At this point, you can do one of two things; go forward and stand on the platform with him so that when he transforms, the blast blows you a safe distance away, or you can run backwards yourself, whichever way gets you the safest distance away from him. The first option is illustrated in the screenshot below.

As soon as the Dragon appears, refer to the strategy of your liking.

Standing behind the pillars is the best way to avoid the dragon's fiery breath. This will give you a good opportunity to shoot him with as many grenades as you can. It takes 12 grenades to bring the Dragon down. The screenshot below shows the safest place to stand.

Whilst standing here, you can attack the Dragon by side-flipping to the left, out in the open where you will get a clear shot of him. Once you have shot him, he will begin to inhale. That's when you side-flip back behind the pillar, in order to avoid the flames.

Side-flip in and out whilst shooting him, and eventually you should have the dragon temporarily down.

If you wish to confront the Dragon head-to-head, the best weapon is the Uzis. Once the Dragon transforms, he'll come straight towards you. It is very important you do not come into contact with his claws, or else, you're dead. It is also important to face him directly, so you will be able to side-flip parallel to his breath, easily dodging the flames. Maintain a constant firing rate whilst avoiding the flames. Running behind the Dragon is also another good idea. It's best not to fall into the water, because it's very hard to get out without getting set alight.

If you do happen to catch fire, make your way to the water as fast as possible. I wouldn't suggest going into the water other than when you catch fire, because it's not necessary unless you're going for a perfect item score. So in other words, avoid getting set on fire.

Once you have stunned the dragon, immediately run towards his belly and press Action. Sometimes, Lara won't perform the action, and might take a few tries. A good idea would be to save your game the very same second you stun the Dragon. This will give you a better chance of pulling out the Dagger without having to bring him down all over again. To avoid missing the Dagger, try running straight into his body whilst pressing Action.

Once you have succeeded, you will have pulled the dagger out of his heart and turned him into a skeleton. Congratulations, you have just defeated the final boss of Tomb Raider 2. Now you had better get the hell out of there...

Make your way towards the exit door, and run through the passage. Make sure you don't stop running, because if you do, it is more likely that you will get hit by the collapsing roof tiles. Even running and jumping is an option. Once you have bypassed them, keep running towards the end of the passage until you are clear.

By EscondeR: To kill the dragon fast and safe I've used this method:
Make it "stick" to one of the columns with it's head and one of the paws, so it can't breath fire on you.

By jeffareid: Dragon's Lair using the pillars for cover. As posted in that picture, Lara doesn't need to move at all. She can shoot the dragon near it's hind left foot.

By fallenangle: As I guess many people here know it is very possible to take down the dragon without moving at all from beside the pillar is you're positioned correctly. If you're in one particular position you can get the dragon pressed against the opposite side of the pillar into a repeating cycle, raising it's head to breathe fire but not being able to hit Lara. However Lara can lock on with her guns momentarily - in this way it's a long but easy job to take it down just with the pistols.