I would suggest a Ranged Primary, Telesto or maybe Jotun (with Particle Deconstruction mod), and then likely a Heavy Linear Fusion or maybe Lasting Impression (so you don't blow yourself up in tight spaces) Rocket Launcher. I like having an Armour build that allows me to make War Mind cells so I can suppress or burn enemies and Heal myself if I'm running a Titan or Hunter build. Edit. This loadout would be for next weeks Fire Breathing Knight Boss.

Basic build: Passive guard, protective light, charge harvester, lament, devour warlock. Armor exotic of choice: astrocyte verse This lets you basically solo everything

Loadouts that worked for me have been Trinity Ghoul/Sleepless, Salvagers and Sub Zero Salvo. Key is being patient and using the front cover area as best as possible. Get both bosses down at the same time, when one hides in the back focus the front/right one down to like 10%. Make sure you control the adds, go to the top left and hide behind the cover and finish up the hiding boss. After that the front/right boss won't take too long to kill. They have to die close together otherwise the number of adds and axion bolts increase. Ironically this was the first boss I achieved solo flawless on. Some modes don't require fusions but tried and true weapons.