Conference Call, and a Bee Shield when the Tentacles come up, and apart from that, a good assault rifle and submachine gun that you can hammer away with.
Youre going to need to exploit the map, where the spot on the rock makes you invulnerable to his lash attacks, and will block the spikes. Its a cheap move, but if you want to solo this beast, you gotta do it. Otherwise youre just gonna get b-slapped off the mesa, or nailed by tentacle projectiles because youre the only target.
For the Rocks, and Beam attacks, you just have to burn those tentacles down as fast as possible to keep from getting downed, as the spot on the rocks doesnt help much with those attacks.
Pack transfusion grenades to restore health in a pinch, and keep an eye on that health so that if it gets low, you can use the turret to throw out just before you go down so that it can help you drop a tentacle and get back up on your feet.
The Seraph Relic that regenerates health is a nice relic, and youll need to spec into health regen while shields are full, as well as health regen upon damaging an enemy to help keep you going.
After that, its all about patience and survivability. Youll need some luck for sure, but it is possible.