The statue angel was a spiritual life form meaning she had only one direct weak point, that was her core-her dependence on material body was almost non existent at this stage. Cores were basically the heart for these spiritual life forms.
Extreme Spirit Body damage could also weaken them, but that's a more indirect route. This reason along with their perfect resistance against attacks with less spiritual damage made spiritual life forms hard to kill.
Finn was able to deal damage without it being reduced, but the Angel was more adept in combat even though she didn't have a Gift.
But she was clouded with madness and her body was still stiff from being a statue for more than a thousand years. This added to Finn's hope of being able to make it through the fight.
From within the iceberg, the statue angel forcefully broke the ice. This also caused the webs tangling her to break.
