The Last Giant is fucking WRECKING me...damn. I've only been leveling endurance (started as swordsman), so my vigor is only 4. That might have something to do with it, but the fact is that even with all that endurance, if I manage to block a hit, all of it is drained and I'm staggered. Cray cray. Also Pate can't do shit against him.
I'm assuming this is the first boss most people face, right?
It was the first I faced if you don't count the initial Pursuer encounter.
Just circle around his legs and slash when you're behind him, watching for his stomps and backing away accordingly. The only tough spot is his swipes when you're caught in front of him, but just roll between his legs as he winds up and you're fine.
Try locking is right foot and staying behind it. In general it is safer than the left foot for some weird reason.