The boss arena has three "islands" which you can access via jump pads. The Pegasus will begin bombarding your current island with an electricity attack, and you must damage it while it is flying overhead. Any weapons will work, however, the redeemed hands do great damage and can lock onto the Pegasus making them the best option. If you've done enough damage, Pegasus will and on your island in a stunned state, and you must damage it as much as possible with your specialist weapon. After Pegasus rises again, immediately leave the island, as if you have done enough damage, being on that island will now instantly kill you and you must escape before it does. That island will then become inaccessible and a max ammo will spawn.
Repeat this step until Pegasus attacks the warlord in the center of the arena. You will now be restricted to one island, and you will have to fight off waves of zombies. In the middle of this, the warlord will jump to the island and attack you. You must damage him enough while he is here to put him in a similar stunned state to Pegasus, and once in this state you can damage him with your specialist weapon. Repeat this until the warlord dies and drops a key. Interacting with the key will start the final cutscene.