Weapons I would recommend:
1: Fire Lyuda. Depending on your exact build it can kill him ludicrously fast.
2: Wedding Invitation. Can utterly wreck GW. It’s got the advantage of being more ammo efficient than the Lyuda and always fire elemental. Since GW is easy to hit criticals on, you are not likely to run out of ammo.
3: Maggie. Just a very solid gun overall that will do great damage on crits.
4: Bekah. Does a lot of damage.
5: Kings Call, fire. Excellent damage on crits and also very ammo efficient.
6: A low-level Sellout pistol and an elemental projector relic. If you are running a spiritual driver COM, you don’t need the Sellout (make sure to have your action skill element set to fire). Just light yourself on fire with the elemental Projector equipped for your damage to skyrocket as long as you are using a fire weapon.
7: A Dictator, fire. A bit more difficult to use properly but it can put a stupid amount of bullets and damage into Graveward.
Additional advice: Not all of Gravewards critical hit spots are equally vulnerable. His eyes actually take the least damage and you should only aim for them when GW has his face planted onto the arena. His chest makes for a pretty good target, particularily because it is exposed whenever he tilts the arena or is knocked down onto it. His greatest weakspots are revealed only for a short period of time whenever he slams his arms onto the arena and shoots out those radioactive orbs. Whenever he does that, give him everything you got.
To avoid falling off the arena when he tilts it, just keep on bunnyhopping, whilst at the same time aiming for his chest.
Don’t bother with the adds, just try to avoid them as long as possible. As long as you keep on moving they usually don’t give you too much trouble and you can try to keep the weak ones alive for when you need a second wind or your kill skills active.
Graveward is, as you may have gathered by now, all about his critical hits. If you can’t hit them, don’t bother shooting and wait until they are exposed, save your ammo. I would also recommend you make sure that the map didn’t roll additional bonus health or reduced damage from critical hits as Mayhem mods, otherwise it can take ages to kill him.