When you reach Capek's Inner Sanctum, there will be a few guards with heavy armor. Try and take them all out, except for one because as soon as you do, Capek appears. Run to the ramp on the right-hand side of the room and take a right at the top of the ramp to follow another ramp up towards a door. Arm yourself with the Assault rifle and take out the last guard. As soon as you do, Capek appears and Eos blasts through the door where you are standing. Run through the hole she made and you will find health and weapons. Save your game at this point. Then, use the assault rifle to defeat Capek. However, stay away from Eos because if she dies the fight ends.
After defeating two of the three guards, run up the ramp to your left and take the gun and ammunition. Then, kill the guard on the opposite side. Capek will immediately descend from above. At this point keep moving -- do not try to fight him, but stay on the ramp. Eos will break through the door where the third guard was located and begin shooting Capek. Quickly run through this door and pick up the sniper rifle and ammunition. Then, back up so that you are out of Capek's sight. When you go back to the doorway, you will see that Capek has ascended back up to where he dropped down from and Eos is running around shooting at him, but he is not firing back. Stay in the doorway, take out the sniper rifle and shoot his protective purple bubble five times -- do not worry, he will not shoot back. After five shots, his bubble will burst, he will drop down to the platform below, and begin shooting at you again. Leave the doorway and begin shooting him with one of your automatic weapons. That combined with Eos' shooting will defeat him easily. Note: As you are running around, stay away from Eos -- if Capek's projectiles miss you, they will hit her and your game will be over. Capek never tries to hit Eos; he just wants you.
When you first enter the room were Capek is located, take out all the guards and he will appear. At the same time, a wall will blow open and your girl partner will arrive to help you. At this time Capek will try and hit you with his weapon. Even though your partner is helping, Capek will only shoot at you. Move into an area were you know he will not be able to find you and remain there. Your partner really does hurt Capek when she fires. It may take a few minutes, but if you stay there your partner will take out Capek for you. Note: You might need to return fire.
When you get to Capek's lair, after he appears and starts shooting, go back through the door you entered and stay there. Eventually, Eos will kill Capek herself and she will not die.
You can also defeat Capek by running up the ramp to the platform directly underneath him. Use your shotgun in automatic mode. You will have to reload once or twice, but if you can avoid getting hit by him you will defeat him.
