To safely defeat Wesker in his first form quickly, run to all the levers around the map to turn the lights off. Don't go up the ladders because there are no levers up there. Don't try 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 while trying to find you. When this happens, take the opportunity 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 ammo, send Sheva to fetch it or 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 avoiding his attacks. After he takes a certain amount of damage, he will go after Sheva. At this point, run down the ramp from the circular area you were just in a nd 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 is defeated.
During Wesker's final form and after saving Sheva from Wesker and pushing the boulder over to allow her to join you, you will once again be attacked by Wesker once you run to the higher ground where you faced him earlier. Like before, dodge his attacks as you shoot his heart, which switches 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 several 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, just 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).
Use the following strategy to defeat Wesker's final form faster. Note: An RPG is required. 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 you connect a hit, the game will immediately advance to the final cinematic.
To easily defeat Wesker in Chapter 6-3, when you appear on the volcano, run away from Wesker until the bridge breaks. Then, have Chris stay as close to the edge of the land as possible before jumping across. Do not shoot or do anything else. When Wesker gets close to Chris, the cinematic of his back will play. Have Sheva ready with a rocket launcher and shoot him as soon as possible, in the white spot.