Let's analyze Hunter's behavior during the Eclipse lake episode, because there is a lot to unpack.
First, Hunter asking Belos about the rain in the human realm. It's such a simple but effective way to show Hunter's age. To show him ask an innocent, curious question like the child he still is. A child that was groomed into the perfect servant since he was young.
At the very beginning of the episode, we actually see Belos' softer side towards Hunter, the times when he actually smiles at Hunter and puts a gentle hand on his shoulder and tells him stories to sate his curiosity. Times where Belos actually seems like a caring parental figure. But even then, we see his true nature slip through when he talks how "Everyone has a use" and "It would be such a hassle to find a replacement."
And as we see throughout the episode, that last line hit Hunter really hard, it instilled a fear of what might happen if he fails again, and that fear is his driving point the entire episode.
As Hunter tries to appease his uncle, we see him almost directly quoting what Belos had said to him many times, "I swear I can do better." It is clear that Hunter takes to heart and internalizes everything Belos says to him, to the point that he repeats it as he talks about himself.
Even at the beginning of the episode, near the caves, we can see Hunter's composure cracking, showing his desperation. But he quickly masks it all with a hopeful and upbeat demeanor and a forced smile.
One might think that when Hunter talked to Amity and told her that Luz' message is a threat that he was purposely planting seeds of doubt into her so that she can sympathize with him enough to later let him go, and it is partially true, but he is not maliciously misinterpreting Luz' messages as threats. Taking his upbringing and the way he acted during the whole episode into account, he genuinely believes that those are disappointed messages urging Amity to do better. He clearly thinks he is only bringing to the surface what is already there. He is looking at Amity's relationship through the same lens he uses with his relationship with Belos. A person with no frame of reference for what a healthy relationship looks like is going to see the slightest setback as a disaster. "There is nothing worse than disappointing someone who thinks you're special."
"I'm an awesome girlfriend."
This shows how Hunter is desperate for affirmation. He does not think he is enough unless someone explicitly tells him that. It implies that Hunter may have had moments where he thought he did good, only to be told that he wasn't enough, that he can do better.
As he trips up Amity and runs away, you might at first feel like everything he did up until that point was an act, but really, it's just a case of using your situation to the best advantage. His desperation as he pleaded with Amity to release him was not an act, it was real. But once he was free, he decided to buy himself the time he knows he'll need to finish the mission, and trips up Amity and runs away. Besides, he was literally a hostage, the only reason we're mad at him for this is because it was our heroes that did it.
You can be mad at Hunter for betraying Amity's trust in the lake scene, and Amity has every right to be angry too, but considering his circumstances, his behavior makes perfect sense. We all know from the scenes and their implications in Hunting palismen that his fears of what Belos might do to him if he disappoints him are completely warranted. It was all done out of a desperation to remain useful, because he knows what happens when he isn't.
It is literally a survival instinct.
So when he doesn't find the titans blood he needs, when he's exhausted all his options and he realizes that it's hopeless, he has a legitimate mental breakdown. He uselessly digs into the dirt, an instinctual attempt to still somehow fix the situation even though his rational mind knows it's in vain. He laughs as he proceeds to dig his own grave in some kind of morbid coping mechanism. It's all a frantic cry for help that he does not expect to get answered. Once again we see him repeat what Belos said to him "Everyone has a use, and if you don't, bye bye." The line "That's just life." further indicates how he has lived under this mentality for so long that he thinks it's normal.
His resignation is visible in what he says to his palisman, "Go find a better witch to be with." Someone who isn't powerless without his staff, someone who isn't useless to the only family he has.
This is where Amity has a chance to talk to him, tell him that she truly understands how he feels. That he feels like he has to justify existing. "But there are people out there who won't make you feel worthless. You just have to let yourself meet them." because she did. And he can too. And it really does seem like her words may have resonated with him a bit. It really looked like Hunter could have had some acceptance of Amity's help, if only because of a "I have nothing left to lose anyway" mentality. It is unrealistic to think that this could have been Hunter's turning point. What Belos did to him is so ingrained into him that it is going to take time for him to fully realize the truth and come around.
On a side note, we see that his palisman is the first part of that support system he will build for himself, and it seems he will also serve a role of guidance, as indicated by him sitting on Amity's shoulder as she offers help.
Here it is important to note that Amity already has a support system, people who truly care about her and won't cast her aside if she fails. Hunter doesn't. He grew up in complete isolation, dependent on his uncle. He doesn't have anyone beside his uncle who knows and "loves" him, someone to turn to. Without his uncle he has nothing. Without his uncle, he is nothing. Even if Hunter builds the support system he needs, leaving Belos will still be hard because he is still the only family Hunter had for a long time.
So when he sees the key, that desperate hope is renewed once more. He can still be useful to his uncle.
Look at his focused yet somehow empty look. That is not determination or malice. It almost looks as if he is dissociating into a strange tunnel vision.
As he fights Amity, we continue seeing that delirious desperation in how he hyperventilates as he erratically teleports around.
"If you really wanna help then give me that key!" because a few nice words won't fix the issue, they won't make him useful to Belos. No, the key is the only way to fix this. And he has to fix this.
But he's tired, he knows he won't be able to win, but he needs the key, so he uses the one card he still has, threatening Amity and everything she cares about.
When Amity gives him the key, he tells Amity he appreciates that, genuinely meaning it. He seems to actually be a bit apologetic that he was driven to this. But he needs the key more than she does. If what she said is true, she won't get thrown aside and replaced for her failure, he will. What Amity did, it might as well have saved his life in Hunter's eyes.
Even so, it seems Amity's words have come through to him a bit, as he seems contemplative as he holds up the portal key. At that moment his palisman shows up, and he is, albeit surprised, genuinelly grateful that he stuck with him. And it is at that moment that Hunter starts to accept his palisman as his friend, and it is at that moment they start to form a bond and Hunter can understand what his palisman is saying to him. There are people out there who will love him unconditionally.
"You just have to let yourself meet them."
As a sidenote, I just wanna point out that by explaining Hunter's actions I do not mean to insinuate that it justifies them. "Trauma does not justify doing bad things" and "Abuse victims have a warped perception of reality and thus will not always act perfectly or innocently, as well as do bad things out of desperation and cause it's all they've ever known" are ideas that should coexist, otherwise we are demonizing abuse victims and making them feel unworthy of the help they need.