With his dragon hand in there are just a few more movements to elden ring weapons pay attention to. The most dangerous of them is the dragon breath that has an enormous area of effect that can be sprayed multiple times. The telegrapher communicates this threat by raising the dragon head into the air as its mouth starts to let out flames. Make sure to move to the opposite side to avoid the force of the blast. The other one is the fiery rock assault, which can be seen by him dragging his dragon head around his body in an circular motion prior to blasting fiery rocks into the air. You can chase him and let the rocks float through your hair, or simply get away and heal and let the rocks burn on the ground.
If you feel more certain, you could equip the Gold-Pickled Foot and use it prior to taking down Godrick to get some additional Runes. Defeating him will get you the Godrick's Grand Rune in addition to the Remembrance of the Grafted (See our guide on ways to replicate Remembrances).
Rest at the new Spot of Grace here to increase your level, and then talk with the NPC earlier, that is now tromping on Godrick's grave. Then, continue up the path and go into the temple, and you'll be able to see Godrick's his throne. The door is to one side of the King to find a second chamber where you are able to speak to a ghost who laments the utter failure of his services to a maiden. Grab the Shabriri Grape close to him, and then proceed to the temple exit which spits you out to cheap Elden Ring Runes the next area, Liurnia of the Lakes.