hi, sorry if it's been asked before, but what is the trigger to being able to cross into the castle in the "troublesome slimes" quest? i've searched the entire cave map for it but i've found nothing
The quest starts in Submission, not the Bat Caves.
When you first enter Submission, you are greeted by Claire and are handed the starting mission. If you somehow hacked/debugged your way past this, go back to Lilaya's house and then enter the sewers normally.
Now, hunt the 'alley' tiles in
Submission until you find a slime NPC, you don't need to fight the slime NPC, but unless you want to become a slime, lay the smack down on them.
After beating the slime, return to Claire and there should be a button that says Report Back. Click on it and Claire will give you the second part of the quest, which is to find the Slime Queen and put a stop to her activities.
Go back to the Bat Caves and go to the castle by boat or fly there if your character has wings. Beat both fights, talk to the slime queen, then go back to Claire and the quest is finished.