Tyrant's Pit is a post game mode where you can fight all three bosses in a single go. It's a good challenge, one that can unlock the trophy/achievement Bold and Bossy.
For those trying to beat this on Tyrant, or lower, difficulty there are only a couple things to keep in mind.
I used Little John with Double Punch, All or Nothing, Feeling the Heat, and the combos Iron Uppercut/Iron Palm Thrust. I would also get Parry since it helps a lot to have.
When fighting Guy it helps to remember he follows a predictable rotation. This is bombs, chain gun, laser, and then jump/repeat. One helpful trick is staying close after bombs will almost always result in him doing a leg slam. Just jump/dodge and you should be good.
Guy ultimately comes down to not getting hit by the chain gun (it can kill you in a single go with full health), and being aware his bombs have a slightly wider radius than shown.
Red Roger is, by a wide margin, the hardest fight of the three. What makes him so difficult is Prioress of Kirklees can do a lot of damage very quickly, along with her attack frequency increasing as her health decreases. She is also prone to an annoying glitch where she will float back mid-revive making it impossible to get a good damage phase in.
For this reason I strongly suggest saving your Overheat and smacking her with it. When done perfectly you should be able to two phase her, though three is also fine. I also never had Red Roger revive like that, so if it happens to you remember to attack.
While it's probably obvious, I never developed a tactic to defeat the Sheriff. It helps to parry as many attacks as possible, though it's so much easier to just burn his health. Even with the terrible performance it didn't stop me from getting S rank overall. That said, if you do need additional tips please feel free to comment below!