Champion Gundyr is blocking your path to the mirror version of Firelink Shrine in the Untended Graves. He's an optional boss, but given that there's some cool stuff at Firelink Shrine it's worth it. There's heavy speculation that this is a version of Gundyr from the past, since he's harder, better, faster, stronger than the guy you fought all those hours ago.
1. The Approach
The run through to Champion Gundyr is harder than the one to Iudex Gundyr simply because you have to start way further back in the Graves. If you stick to the left hand side more you should be able to time your run to avoid the tougher enemies and then make it out and down to Gundyr. This version of Gundyr is weakest to frost and lightning damage, and you can get good damage in with fire as well. If you have spells that do these, or buffs you can stack on your weapons, then apply those. Champion Gundyr's damage is physical (he just hits you real hard, man) but, like the first Gundyr you fought, he can be parried.
2. Champion Gundyr's first phase
Champion Gundyr has basically the same moveset as Iudex Gundyr, but there are a few extra attacks peppered on top, and the whole thing is performed faster and with more aggression. Gundyr can grab you with his free hand and impale you on his halberd, before throwing you half way across the arena, but the most annoying new move Gundyr has is a dainty looking high kick for if you've gone in around the side or behind him, which would be funny if it didn't knock you back and leave you stunned on the ground, open for attack. It means that melee players can't dig in away from his weapon to get cheap hits in, and you have to keep moving in and out.The fight in general is a real stamina drain, especially for melee players, who'll have to dodge or block a disproportionate number of times for each hit they land.
Fighting at range requires that you have your timing absolutely nailed, since Gundyr will leap at your more frequently than he used to. It might take you while watching him to be comfortable with the distances he can move and attack from, stacked against how long it takes you to perform your own attack.
The right hand side of the arena is still open and unwalled, so it's possible to roll or be hit off the side to your death. If Gundyr manages to grab you at the right angle he can throw you clean over. Wipeout.
3. Champion Gundyr's second phase
In this phase you need to play even more cautiously. Gundyr's eyes will start glowing red, which you should know by now is a bad sign, although he doesn't suddenly become on fire like a lot of the other bosses, so... every cloud. He'll now move much and attack much faster, as well as hitting harder. It's not a good combination.
Gundyr will now start chaining more attacks together, which makes it harder for melee players to get an opening. When you do you shouldn't be trying for more than one hit, two at a push, or you'll pay for it. If you keep further back you can bait heavier smash attacks that will give you a little more time to attack. Ranged players should be aware that Gundyr will charge and jump a lot more to close the gap in this phase. It's a case of running, assessing what he's about to do, and deciding whether to risk a ranged attack or run again.
This fight can be tough, and requires a lot of movement, but if you've gotten this far then you can kick this guy's ass for a second time.
Buy the official Dark Souls 3 Guide now.