Move right and you'll see a pit. The opening stage of this round has several of these pits, which you can throw enemies in and defeat them instantly. There's a catch though: if you defeat them this way, you won't gain as many experience points as you would if you fought them normally. Also, you need to be careful about standing around near the pits, as enemies can knock you down them. If you fall into one of the pits, you'll lose a life.
Once you move past the pits, there are more Mad Gears to take care of, including a few El Gados. Once you've defeated them, you'll head inside a building, so head right. Watch out for Poison, who'll drop down from above. You'll also have to fight J and several Breds here.
Defeat them and then some barrels will roll on. Destroy them to reveal some useful items. Keep going and fight Poison a couple of El Gados, and Bred. Once they've been dealt with, you'll drop down a hidden passage.
You'll drop down into a ring, where Abigail is waiting for you. He claims to be the toughest fighter in the Mad Gear, and after some trash talk, he'll start to fight you. He has an attack where his head will flash for a few seconds, then he'll charge and try to do a punch. Use a jump kick to knock him down, or just get out of the way. He also has a grab move, where he starts kissing you! This can do a lot of damage, so try not to let him get too close to you.
Never try jumping at Abigail unless he's charging. He's got an anti-air uppercut attack, which he'll always hit you with before you can hit him with a jumping attack. What you need to do is wait for him to use his charge attack, and use a jump kick to knock him down as he charges. This will take a while, so what you can also try is getting out of the way of his charge punch, and as he misses, go in and throw him.