A cutscene will appear that you are now fighting against the first major boss, Cerberus the Ice Guardian.
Crystal Geyser: Cerberus will use this attack often, sending rows of crystals trailing towards you
It's Raining Icicles!: Cerberus' head with yellow eyes will howl and cause icicles to fall from the ceiling. White cracks on the floor will tell you where they'll fall. Side rolling or dashing should easily avoid this. NEVER TRY JUMPING AWAY FROM THIS
Bark-a-glacier: Cerberus' head with blue eyes will send a huge chunk of ice across the battlefield. Run to the extreme corners of the room to escape it. You can also slash it in half with a melee attack or guard it with Royalguard to get Red or Green Orbs. Both require good timing. This attack also has a relatively long warm-up, so if you're close you can whack at his legs while he charges it. If Cerberus enters berserk mode, then he will blast three ice boulders at the same time
Skating Rink: Cerberus' head with red eyes will breathe cold air on the ground, freezing Dante if he stands on it. Run to the sides to get out of the way, or jump, Air Hike, and use Ebony & Ivory or Aerial Rave to stay in the air until the ground melts.
Head butt: When Dante is close and in front of Cerberus, he will lower his head and attempt to push him back. This can be hard to avoid if you're directly in front of him, so avoid attacking from there. Sky Star (Level 2 Trickster Style) or Air Guard (Level 2 Royalguard Style) are the best at dealing with this attack, but you won't have either yet on your first play-through.
A Man's Best Fiend: Cerberus will shake loose his restraints and leap to the far end of the room to deal MASSIVE DAMAGE. Stay to the extreme edges to avoid this. You can attack his legs and heads as he is dragged back to the doorway, or try million slashing his legs for stylish points, then real impact if his ice armor is shattered. It's particularly advisable to stand in his armpit, as this will allow you to be dragged back with it so you can continuously attack him.
Paw Swipe: Cerberus will slash at Dante with his claws. Jump up or dodge back, out of its range. His left arms deals lighter damage, but it's pretty unpredicatble, while it's vice versa for his right arm
Ice Age: When Cerberus rears onto his back legs and howls, he regenerates his lost armor.
Berserked Million Carats: Cerberus stands up with his hind legs and stomps the ground. The area near him will sprout out frozen spikes like the Crystal attack. This attack is extremely painful. Avoid standing near him or you could stay airborne with Ebony & Ivory. He will shout "You're not human are you?!" before doing so.
Cerberus is covered with ice that must be removed before he can be harmed. Use Ebony & Ivory or the Shotgun to remove the ice armor. Use the R3 button to change your lock-on target to the next head or leg once you've cleared one, because the less ice that's on him, the more damage you can deal.
Once the ice is off, it's time to be daring and charge at them head-on. Jumping in with Aerial Rave (Swordmaster Style) or Helm Breaker to deal damage, but Cerberus will try to push you back if you stay too close. Slashing at the legs deals less damage, but it can cause Cerberus to fall down. When this happens, jump in and start attacking the heads. If you can, slash all the three heads at the same time. This will multiply the damage.
Air Hike would be very helpful in this battle.
You can also keep firing Ebony & Ivory or Shotgun from the corner. This method is safer but it is time consuming. In a similar manner, you can Wall Hike and then Wall Run to get significant altitude, then fire Ebony & Ivory on the way down. This keeps you safely above all of his attacks except the Falling Icicles.
Upon defeating Cerberus and finish watching the cutscene, Dante will receive the Cerberus Devil Arm. Head towards the door to finish the mission.
When replaying this battle in future playthroughs, it is generally advisable to have Agni & Rudra equipped because not only does Cerberus have a weakness for fire-based attacks, but also because Agni & Rudra's movesets have more applicability for the contingencies the battle brings. For example, Whirlwind can be executed fully to propel Dante upwards, perfectly setting him up for and Aerial Cross or two before hitting the ground, dealing significant damage.