[2023] PLEASE STOP ADDING TO THIS THREAD WITHOUT READING IT - Ballast Flora is Invincible after it takes over most of your ship

You need to start purging Ballast Flora from the outer reaches, the more it spreads the greater the roots health or rather health regeneration gets. To make purging faster you can severe its growth, severed part of the flora which isn't connected to the root will dry up and die. But its safer to just start killing the growth from the outer reaches and pruning it towards the root until the root is killable.
However IIRC you should be able to kill the root with a long lasting fire or plenty of grenades no matter how big the flora has grown.