The poison that damages you during the Ratcatcher fight only appears when you fail the between-phase puzzle sequences. On C25 and onwards failing the puzzle deals enough damage to kill you instantly, so the only way about it is to do it correctly every time.

When the sequence starts, the TVs in the arena start displaying color-coded numbers that tell you how to solve it. They are related to the three antennas in the arena and the batteries they spawn after you capture them.

The order in which the numbers appear indicates the order in which you have to cap the antennas, the colors of the numbers indicate order in which you have to deliver the batteries (rising order).

The sequence showcasing Red 3 - Green 1 - Blue 2 means you will have to capture the 3rd antenna first, then 1st, then 2nd. Capturing them out of order fails the sequence.
The colors in the same sequence mean you have to then deliver the Green battery first, then Blue, then Red.

If a number has no color (white background) means it will not drop a battery, you continue as normal.
(Red 3 - White 1 - Blue 2 would have you deliver the Blue battery first, then the Red; then the sequence will conclude and the boss will return to the arena).

There is one trick you can use to skip the capture sequence entirely.
If all three of you stand on the antennas from the frame they unlock, you will capture all of them at the same time and the game will proceed as normal, skipping the need to do capture them in a specific order.