To clear phase one of the fight you have to wait until an npc, that you have to protect, gets evacuated from the boss room. It doesn't matter how much damage you do in this phase, it's effectively on a timer. Though you can speed it up by doing simultaneous damage to the two bodies of the boss, this also provokes voice lines from the boss. Because you have to wait for the voice lines to finish before phase two most speed runners prefer to avoid doing damage and focus on defense which is slightly faster than waiting on the voice lines. However it can be safer to focus on damage as it can interrupt attacks focused on the npc. The worst situation for a speed runner though is when they attempt to cause simultaneous damage, and fail, as there are separate voice lines for both doing damage, and successfully causing simultaneous damage.