To quickly and safely defeat Wesker in his first form, run to all the levers around the map to turn the lights off. You do not need to go up the ladders because there are no levers up there. Do not worry about attacking him until you have turned off all the lights, otherwise you will not be able to hit him. After all the lights have been turned off, take the rocket launcher in the display case after breaking it open. Run to a dark corner far away from him. Wesker will look around to try and find you. When this happens, you will have a chance to shoot a rocket at him. As soon as you shoot it, he will grab it. Run up to him (or shoot the rocket in his hands), stun him, and initiate a button context. If you need more ammunition you can send Sheva to fetch it, or you can get it by climbing to the area above the ladders. The second form is nothing but a button context scene battle, and there is no specific strategy needed. In his final form, start by running to the high ground. Then when in the circular area, shoot the orange "heart" that alternates from his chest to his back while dodging his attacks. After he takes enough damage, he will go after Sheva. At this point, run down the ramp from the circular area you were just in. Make a left to arrive at a large boulder. Instead of interacting with the boulder just yet, shoot Wesker from afar, while Sheva hangs in the balance. Once she lifts herself up, start to move the boulder using the button contexts. Make your way back to the high ground and repeat the orange heart strategy until he has been defeated.
Use the following trick to defeating Wesker's final form. Once you have saved Sheva from Wesker and have pushed the boulder over to allow her to join you, you will once again be attacked by Wesker, when you run to the higher ground where you faced him earlier. Like before, dodge his attacks as you shoot his heart, which alternates between his chest and back. Once you do enough damage to his heart, he will kneel down and push his arm into the ground. It then comes up around him as many swirling tentacles, protecting him from fire. If you wait and do nothing after he gets back up, you will see a cinematic of tentacles recovering his heart, which you do not want to happen. To prevent this, as soon after the swirling tentacles recede, run up to him and there should be a button event will begin, allowing you to hold him while Sheva stabs him (and later you), which is how you can finally kill him.
Use the following trick to defeat Wesker's final form faster. Note: It requires a RPG. It is easier to do with Sheva, but still can be done with Chris. When Wesker is going up the incline to the center area while chasing Chris, fire the RPG at the orange point on his back. If done correctly, the game will immediately advance to the final cinematic.