just hit it until it change element? or go super bloody palace is super free

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make sure backup data on stage 89, then use his pistol and make distance from that boss

Use the warmup to practice. Single jumps for the falling ice chunks because air hike doesn't have iframes. Watch out for the ice rain. Getting away ASAP is the way through it I think.

The easiest way to get the boss down is to learn its attack patterns and hit-boxes (like most bosses). That way you will get way more comfortable regarding when you want to use your i-frames.

For this boss in particular as Nero, its generally best to approach during fire and ice forms.
When the boss starts, he will generally just use some basic attacks and a pounce, and this is where you can rack up damage.

Eventually he will change to electric-based attacks, and this is the more tricky part for Nero if you don't know what youre doing when fighting him melee. Therefore I recommend just camping this form out. If you DON'T approach, he will spam the same two attacks until he eventually change form again.
One attack are a bunch of electric orbs. Charge up Blue Rose once and use your 3 bullets to clear most of the orbs. The reason you need to charge at least once is for the AoE hits, thus being able to down multiple orbs in one shot.
The other attack is a ground slam that, after some delay, electrifies certain lines on the floor. Get the pattern down and use I-frames OR tripple jump to evade.

The third form is the ice form. If you stand at a distance, there 2 possible attacks he will do.
The one he does more often is the icicle rain. This one homes in on you, so keep on the move with air taunt or i-frames to avoid.
The other move is an ice breath. Very easy to avoid, so won't comment on it, other than that he does this rarely.
To make make him stop spamming these two attacks, you need to get to the "inner circle".
Here he will mostly get back to doing the same standard attacks as in fire form, use this to rack up damage.
HOWEVER, there is one additional attack he does which is ice rain. You see he will do this when all 3 heads are looking downward whilst quivering. Get back to the "outer circle" asap.

He eventually goes back to fire form again, but with one additional attack, a giant pounce that does ton of damage if hit. Get the timing down and this attack won't be a problem at all.

My recommendation in Devil Breaker is Gerbera. While in the air and pressing the Devil Breaker button, it gives you i-frames, thus giving you a "second chance" if you timed a dodge or jump too early.

Best of luck!