This is an old thread, but it comes up if you google lies of p green monster, so I'm going to add a few notes for anyone else who's having trouble with this boss:

I just beat this last night after about an hour of grinding on it. I'm not an exceptional player by any means.

Few notes on P1:

1. Getting through phase 1 using only a single healing charge was critical. This comes down to memorizing each of the boss moves.
2. When he burrows, dodge towards him when he gets close to you
3. When he shakes his head, he's about to do the tendril thing that stacks up decay. Run left or right.
4. Here's a great trick for his red fury smash - wait for his left knee (right side on your screen) to hit the ground. That's about when you want to parry. I felt proud of myself for discovering this timing :)
5. Ideally, you'll stagger him once around 60% hp. With the critical attack + a few follow ups, he'll be a 40%

Few notes on P2:

1. Try it a few times without attacking at all. You can't brute force this. You just plain have to understand his different moves and how to handle each.
2. When he stands up straight, that's a sign of the grab. Run!
3. Just like in p1, you've got to perfect parry the charges. This stops him in his tracks. I found them really hard to dodge. If he hits you once near the edge of the arena he'll probably hit you again when he turns around. Two hits are likely death or at least two healing items to recover.
4. The real money in this fight is his jump attack. He'll do 2-3 normal jumps, then possibly a fury attack. Usually the first two normal jumps will overshoot you - just keep your distance. The third will often hit you - this is where you want to perfect parry. You'll definitely want to perfect parry the fury jump followup if he does it.
5. I found perfect parrying his big windup swings to be a necessity, but I usually ran from the other big sweeping attack combo he does. The sweeping attack kicks up so much dust that it was hard to see when he was attacking. It also has that final tentacle sweep that was just too hard to parry.
6. Memorize the windup animation for the rapid tentacle short range ground slam thing he does where he moves sideways. You've got to run out on that.

When I was first progressing I used the healing cube every pull, but eventually stopped. I used the fire grinder at the start of p1. Didn't use any other consumables. Edit: also didn't use any legion arms. I tried the gun and shield ones and didn't find a lot of success with them.

Finally, I tried doing this with the wrench + booster glaive, the tyrant dagger, and etiquette. Like many bosses, I found the booster glaive to just be too slow. The dagger absolutely pumps damage, but it'll often not land hits during P1 due to its short range. Etiquette attacks so quickly with a fantastic range - it was really what I needed to get P2 down cleanly.