On the first phase, all of Trinexx's heads will attack. The Fire Head will launch several flames, dealing two hearts of damage. The Ice Head will create several ice tiles in the boss room. The main head of Trinexx will occasionally lunge towards Link's direction. The visual cue of when this attack is incoming is when Trinexx's tail is wagging quickly.
The second phase, the shell of Trinexx will come off, revealing a python-like creature. It will run around the room, trying to chase Link.
On the first phase: Run to the Fire Head, stand behind it and use the Ice Rod. Use the Tempered Sword on the head. Do the same thing with the Ice Head, except use the Fire Rod.
On the second phase: Stand to the left of Trinexx's snake form and use a spin attack. If timed right, you'll do a doublespin, dealing an extra hit of damage. One more spin attack and you'll be able to defeat Trinexx.