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Aero the Hedgehog is fought as a boss in Heroes From An Old World. Currently his only actual boss fight has been against Warp, although the two were accidentally pitted against each other.
Warp's Scenario (Inner Forest Base: Courtyard)
Aero will be calm and speedy in this fight, so keep locked-onto him at all times. Aero's ground attack consists of curling into a ball and charging at you, knocking you into the air; this occasionally gives you the Air-Tossed status. Aero's aerial combo will consist of him running at you, curling into a ball, jumping into the air, and doing an unavoidable Homing Attack on you. This can be blocked with good timing, however, and it is impossible for him to use his Homing Attack on you when in the middle of an attack (be it succeeded or failed) with the energy sword.
However, you can force a Reaction Command by Homing Attack him while he does his aerial combo, which leads to the "Aerial Fury" Reaction Command. Pressing the triangle button enough times will lead you to use the Reaction Command "Takedown," which knocks Aero into the ground and stuns him. This can also happen conversely, however, if you are too slow with the button-mashing, so be careful when attempting this. Aero will get stronger over time, so be careful when trying this later in the fight.
When Aero's HP reaches the 3/4 point, he will begin using his signature Chaos Whirlwind attack. Although (from far away) it cannot harm you, it will throw you into the air and give you an immediate Air-Tossed status, which is bad news. This is made even worse if Aero is close to you when he unleashes this attack, as it can be devastating to your HP.
At the 1/2 point, Aero will unleash his Limit attack, which consists of him using Chaos Whirlwind on himself to make him bound around the room at high speed, while also curled into a ball. He is invincible during this charge, so avoid him at all costs while he does this. He will slow down, and eventually stop, which should leave him open for some good combo attacks if you're prepared. He activates this at random after his HP is cut down to half, but it will grow more frequent when his HP is 1/10th of its original value.
Although a scripted fight, besting Aero earns you 1,500 EXP, which is relatively small considering how much Warp should be leveled up by now. However, all EXP counts, so defeating Aero is a good option.
The battle will end when either combatant loses all their HP, or when 4 minutes have passed.