WARNING: SPOILERS AT BOTTOM
There are four stages of the final battle with Apocalypse.
The first one you fight him normally.
The second one you have to absorb "The Power of the Four" from the machine in the center of the room and attack him with the new power attacks (Polaris:Magnetic Blast,Quicksilver:Super Speed,Emma Frost:Mental Blast,Sabretooth:Healing) When he has about 25% health left, you have to you Quicksilver's super speed to knock down the gates on either side and destroy the machines at the end of each hall.
Then, Apocalypse turns four statues into his four horsemen: Abyss, Mikhail, Holocaust, and Archangel. Destroy them and then attack the machine in the middle.
Once the machine is destroyed, you defeat Apocalypse normally like the first part.
That's the end and you get to see a short clip of the X-Men and the Brotherhood leaving in separate jets and then Apocalypse is seen laughing menacingly on the top of a pyramid.