The first thing you should know about HOD bosses, is their weakness.
After you know The Hanged Man's weak, shoot it (obviously).
At the beginning The Hanged Man will use his bats to hurt you, he’ll stop using them after he has less than half of his HP.
If you’re using the auto-reloader it will be very easy, if not you have to shoot the bats so they won’t hurt you.
After the Hanged Man will have less than half of his HP, he will try to approach you,
after 5 seconds he will fly out of your sight and then will push you,
you fall but you manage to grab the upper part of the roof.
You see him again, he tries to approach and attack you, shoot him, kill him.
Congratulations, You just Killed The Hanged Man!!!