Bird wizard has a few attack phases: One where he stands in a corner and casts “damage squares” which chase you along the ground, and one where he stands in the middle and summons flying enemies. You’ll probably do the most damage when he’s in the middle of the room, though it’s also possible to damage him in the corners, if you dodge the floor squares well enough. When he’s in the middle of the room, unload as much damage as possible and ignore the flying enemies if you can– you’ll probably kill them anyway when they get close to your sword-swings, and the floor squares damage them as well.
The Bird Wizard’s attack patterns get more and more intense the more damage you do to him. In the second half of the fight, he will cast extremely large attack patterns, like vertical columns and large x-shapes. Avoid these as much as you can and continue to focus on unloading as much damage during his summoning phase as you can.
After you defeat him, head around behind his throne to pick up the laser rifle, an extremely powerful and accurate weapon necessary for completing some of the puzzles in the game. Then head outside to activate the pillar and complete the zone.