I completed this game following N18p73pwn3r's guide which means my character build matched the one he recommends in his walkthrough. That is a ranged character using Ice Shot and Poison Shot. I used the second method N18p73pwn3er recommends in his guide but I wanted to expand on some of the mechanics of the fight as I had to figure them out as I went and it was incredibly stressful.
There are three types of devices around the periphery of the map. The towers are hard to miss. The Ornathopter spawn points look like covered pipes at the edge of the map, some are "hidden" at the very bottom of the map so be sure to explore all the way to the wall at the bottom. The final type are werewolf gates which are actually in the walls themselves, and, due to camera angle limitations, only exists along the walls on the top. left, and right edge of the area.
When the fight begins immediately leave the center of the map and move to the outer ring separated by the columns. Choose a direction (clockwise or counter-clockwise) and move in that direction for the remainder of the fight. Do not cross the columns into the center area unless you absolutely have to in order to escape being trapped by ads.
In the beginning, ignore Fulmigati, stay away from him at all costs. Keep moving (clockwise or counter-clockwise) to prevent being overwhelmed by ads. The technique I used was Acid Shot followed by several Ice Shots then a hasty retreat. Repeat this to thin out the ads. As you approach a tower or spawn point, retreat extra distance and fire several shots into the spawn before the ads catch up to you and force you to focus on them again.
This process is slow and tedious at first as the number of ads prevent you from dealing much damage to the spawn points. After many laps you should kill one which creates a domino effect as fewer ads gives you more time to focus on their spawn points.
As for Fulmigati, he is most dangerous during the beginning of the fight. His primary attacks fires 3 orange (willo-the-wisp- like) balls which home in on you. When you see these coming run as they do massive damage. I was never successful in dodging the first ball but the other two eventually vanished after several seconds of chasing me.
At some point he stops firing the orbs. I believe it is tied to his health or the towers in the area (if someone can confirm please put in the comments) at which point he starts using attack similar to the gargoyles. He jumps up and an orange ring appears on the ground. Don't be in that ring when he lands. He also has a machinegun attack which he uses at close range but is low threat.
As for Katerina, mine used ranged attack and I buffed with Mirage whenever available. For some reason she never died and I have no explanation for this. She spent most of the fight off my screen but never got overwhelmed by Fulmigati or his ads. I chalk this up to luck and not skill. If you get as lucky as me, let her do most of the damage to Fulmigati.
By the time I got the ads to manageable levels Katerina (and my own stray bullets) had worked Fulmigati to between 1/3-1/2 health which left very little work for me by the time I turned my attention to him. He is not very powerful by himself so even if Katerina contributes little he should pose little threat to Van H once he stops shooting orange balls and his ads are removed from the picture.
In summary: Keep moving. Stay around the perimeter of the area. Focus on the creature spawn points but remember the first rule so you don't get swarmed by ads. Kill Fulmigati last. Keep moving
Hope this helps, especially those of you going into this for the first time on hardcore.
If you have any recommendations to make the guide better or leave negative feedback please provide comments on ways to improve.