The following is a list of every boss find and the recommended strategy. Note: the order in which bosses are fought depends on the player:
Solomon Grundy During the first phase, shoot explosive gel onto the electrical power boxes anddetonate them as Grundy charges at you right before he runs over the wires. He'll throw a raging fit, disabling one power box but causing the other to drop. Once done, scan the sewer grates with Detective mode to make them viable targets, then shoot them with gel. You need to position Grundy so that he runs over a sewer grate, then into the hanging electrical wire. Detonate the gel as Grundy runs over the grate, lighting him on fire. He'll trip up, causing him to run headfirst into the exposed wire. For the last phase, just repeat the same thing you did during the second phase with the remaining sewer grate/electrical box pairing. Note that your punches don't hurt him, and it is easy to roll dodge between his legs to avoid damage.
Black Mask During the first phase simply beat him up while avoiding his grenades and keeping away from the center of the room so you don't get lit up by gunfire. Next will be a gel detonation puzzle, where you have all the time in the world. Once you catch up with Black Mask, you'll spot him standing under some lights. Don't approach him, or you'll die instantly. Instead, chuck a batarang at the far right alarm, causing Black Mask to shoot in that direction like crazy. While he's distracted, quickly break the nearest light with a Batarang and hop into the floor grates. Walk underneath Black Mask all the way to the far right side, then jump out. He won't spot you in the darkness. Toss a Batarang at the alarm on the opposite side of the room, then duck into the floor grate and sneak towards the center grate. When Black Mask walks over you to investigate the noise, perform a Takedown to finish him.
Bronze Tiger During the first phase simply counter Bronze Tiger as needed, then do a cape swing and unleash tons of punches on the stunned Tiger. When Bronze Tiger jumps into the air, immediately roll-dodge out of the way or else he'll land on you no matter what. When his claws get stuck in the floor, just stun and punch him like before. The third and final phase is pretty much the same as the first (and plays very much like the introductory fight against Catwoman). Simply counter three consecutive swings, then stun and punch Bronze Tiger into a KO.
The Penguin This stealth-based confrontation is likely the hardest boss in the game. During the first phase, get the guards' attention by tossing a Batarang, then quickly swing up to a high vantage point. Get the guards alone by luring them with the sound of exploding fire hydrants (you'll have to scan them in Detective mode and toss a Batarang). Once done, use the Batclaw to detach the gatling gun from their backs, which will knock them out instantly. Once the two guards are down, safely grapple to the center beam, where you can glide-kick into the Penguin then perform a Takedown to smash him in the face. Wait until the Penguin has waddled to the right side of the beam; that way, you'll trigger the next phase of the fight on the left side of the room, which is highly recommended
The second phase is similar except for an automated drone that will shine a spotlight on the upper levels, and being spotted even once will result in certain death since there are now three guards with assault rifles lurking around. Once this phase starts, grapple up to the top floor and use a Batarang to destroy the sentry. The resulting explosion will cause the guards to slowly approach the noise, which should give you a chance to isolate one and strip his weapon from him. Once done, split the remaining two guards using hydrant explosions, then take them out and attack the Penguin in the same way as before.
The third face is the same as the second, but now there are more guards and two drones to deal with. If you spawned at the left side of the room by knocking out the Penguin on the right, quickly zip up to the center podium to Batarang the bottom drone before it spots you. Right after, zip to the top floor and destroy that drone right away. The noise will bring the guards up in single file; take the first one out just as before, then quickly drop down to the center beam. Because this is the final phase, you can actually end the boss fight without killing the other guards. Wait until they're all skulking around the top floor, then glide kick into Penguin and beat him until it's over.
Dead Shot Quickly run to the left as soon as the fight begins. Whenever Deadshot is preparing to shoot, take cover behind any of the barrels or objects. Once you reach the spotlight, Deadshot will shoot it down. You can use your Batarang to bring it back up, giving you time as you continue moving to the left. Don't run all the way to the left. Just before the dead end is a spot you can grapple up to. Do so and keep running left, right into the building. Take out the thugs then grapple to the higher ledge. Continue to this, avoiding Deadshot as best you can. Onceyou reach the area just before Deadshot, hit the spotlight with your Batarang to push the light onto Deadshot. This will give you the time to stand up from crouching and use the Line Launcher right into Deadshot, defeating him.
The Joker Once the fight starts, use the Line Launcher to kick into him. Joker will then pull out a pistol. Stay on the opposite side of the barrels, making sure to roll-dodge as Joker's reticle closes in on you. Joker needs to reload every three shots, giving you a chance to run up and punch him when he's distracted. After that, Joker will pull out an electrified baton and start charging crazily at you. Stand in place as he runs towards you, then line launch to the other side of the room at the last second. When you reach the other side, quickly line launch again to kick the Joker. The fourth and final phase combines the gun and shock stick, but you also have a timer from the poison gas that's filling the room. Use the same strategies depending on the Joker's weapon of choice to knock him out once and for all.
Catwoman The first part of this fight is similar to the Bronze Tiger fight; just cape-stun Catwoman to hit her and roll-dodging out of the way if she leaps in the air. She will eventually blind Batman with a flashbang. While blinded, Batman is unable to move, turning the fight into a game of timing. Wait until you see the glint of Catwoman's red goggles and hear the distinctive "shink!" sound, then counter her and quickly cape-swing to stun her, then punch away.During the last phase, several images of Catwoman will start spawning around you. In an effort to psych you out, some of the images will start flipping at you aggressively. Avoid countering the fake Catwomen or else you'll get hit. Only counter when you see the blue-lightning-bolts indicator to get the real Catwoman every time. Cape-stun, punch, and finish the fight.