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This is easily the hardest boss in the game. That's because it's a stealth-based fight, where staying unseen is the most important thing. We're going to break it down into three phases.
1st phase: Get the guards' attention by chucking a Batarang, then immediately swing up to a high vantage point. Isolate the guards by luring them with the sound of exploding fire hydrants (you'll need to scan them in Detective mode and toss a Batarang). Then, when you're certain that you won't get spotted by both guards, use the Batclaw to detach the gatling gun from their backs, which will knock them out instantly. Once the two guards are down, you can safely grapple to the middle beam, where you can glide-kick into the Penguin then perform a Takedown to punch his lights out. 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 hugely beneficial
2nd phase: Same concept, but an automated drone will shine a spotlight on the upper levels. Make sure to play very carefully for this segment; there's no checkpoint, and being spotted even once will result in certain death, as there are now three guards with assault rifles lurking around. As soon as this phase starts, grapple up to the top floor, and without being caught in the spotlight, use a Batarang to destroy the sentry. The resulting explosion will cause the guards to slowly approach the noise, which should give you time to isolate one and strip his weapon from him. After that, you'll have to very cautiously split the remaining two guards using hydrant explosions, then take them out and pounce on the Penguin in the same way as before.
3rd phase: Breathe a sigh of relief: this is the final segment of this fight, and you've just gotten a checkpoint. This is basically the same as the second phase, 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, immediately 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 commotion will bring the guards up in single file; take the first one out just as before, then immediately 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 punch till he gives up.
