At the beginning of this chapter, you may encounter a glitch: Mantis is stuck in a conversation and you can't go beyond his story and / or you can not deepen the dialogue with Nebula and Gamora and you will said to "come back later".
If any of these situations occur The only solution I've found is to play offline or at least do it for this part. Do not hesitate to log out to solve this problem. If you were not disconnected at the beginning of the chapter, you will probably have to start over at the last checkpoint or leave the game and start again (after logging out, of course).
I also advise you to tell Mantis to get straight to the point.
The trophy unlocks just after the conversation with Gamora and Nebula and decides if Nebula stays or leaves.