1) Focus your attacks on her feet.
2) Once you take that out, focus on the Crown.
3) When the Crown's out, her main body defense will drop significantly.
4) Keep attacking her main body--the one called "Princess Shroob"--until her crown revives. Her feet will probably revive before the crown does, but still focus all efforts on Shroob herself.
5) Repeat from Step 1.
It's very tedious and time-consuming, but you can do it. You can't take out her crown until her feet are taken out, and don't bother attacking her main body until the crown's out, otherwise you'll only give her a measly 1 damage point. Don't waste your time on the tentacles at all.
Good luck!