I found it relatively hard because I played Ultra violence on my first play thru.
The Makyr I actually didn't have to much trouble with, here's what I did:
1.stay in air as much as possible.this biatch loves to burn the ground.
2.use plasma gun with the heat blast mod ( I had it mastered) when you have charged up the gun by shooting then you can do more damage.this will kill the fuck out of most things. there are three tiers of charge and your guns plasma will turn red when done charging all three.
3. headshot the drones with the machinegun for plasma ammo.
4.use the bfg ammo for basically a free shot, you only get one in that area.
5. The makyr can only be killed by bloodpunch, here's the trick, when she is vulnerable use the DB shotgun grapple hook to zoom up to her and blood punch.
If you try to reach her any other way she often will recover first.
6. the gun called the Unmakyr is made to kill the Makyr. Blame doom 64 for that one ;P