Easily done vs Singe once fully upgraded. The setup I used was:
Armor set : Bandit+19
Amulet : Vengeance idol. +50% damage dealt when health below 25%
Ring 1: Devouring loop.
Ring 2: ring of the admiral. +15% damage dealt +300% damage received. Doesn't matter because we're not getting hit.
Submachine gun +19 with song of swords mod
Chicago typewriter +19 with explosive shot mod.
Traits at level 20 : Trigger happy, Spirit, Quick hands, Handling, Catalyst, Executioner, Minds eye & Kingslayer
First activate boss fight and die to remove cutscene . Then return to previous area to power up mods and get your health below 25% (screen will have red edge). Outside boss door consume Houndmasters jerky to increase critical damage by 15%, activate Song of Swords switch to Chicago typewriter, activate explosive shot and enter. Singe will almost always shoot a fireball as soon as you enter ,dodge that and unload!!! In the below video I made 2 mistakes & still comfortably beat him. Didn't reload Chicago typewriter, had 65 in the mag instead of 80, & missed with the first explosive shot.