The Coral Siren is fought after entering the mine, raising the sea level, and rescuing Vera to get the Gastro Drill. This siren attacks from the background with three separate attacks, only one of which is a damage phase.
First, when she charges with electricity, she's about to dash through the stage. Drill down and wait; attempting to interrupt the dash just gets you damaged. Second, she will try to hit you with three waves of bombs. The first two waves have gaps that you can fit through, but the third doesn't. Try not to get trapped in the corner, and you will still take damage if you drill into the floor.
The third attack, she will position in front of one of the dirt floors. Wait next to it and she'll jump into the foreground and burn that pile. You can get a few hits in before a flame pillar comes out to the side; jump over that and you can get a few more hits in.
There are no particular cards that will help with this, but getting some Shampoo or Silky Cream upgrades will help bump your damage up.