The first siren can be reached after rescuing Plink and getting Newt Dash. She will summon weak enemies, but her big attack is telegraphed with a few lines through the stage, then very large vines hit the stage there, so make sure to give them plenty of room.
On both ends of the room are switches that you need to climb to with Newt Dash. Sitting on a switch will move the Siren in the opposite direction. Your goal is to move her underneath the sunlight. Note that the sunlight moves, so if you get close and it disappears, it's best to wait for it to get back into position. Once she does, she stops attacking and flowers drop from the ceiling. Jump up these flowers to get in melee range. You really only need to get up to one flower to jump and reach her at the same time.
The only card that could really affect the fight at this point would be Spider to speed up Newt Climb.