The scene with the song "I'm Still Here" accompanied by images of Jim's father leaving him and his mother. Especially the one where Jim runs down the stairs in the morning to find his mother crying, then in desperation runs outside to where his father is taking off on a ship and he tries to get to it before it takes off but fails. The sequence was done beautifully.
Jim stacking plates and overhearing his mother fretting over him; the guilt and frustration with himself is obvious, and anyone who's ever seen their parent at their wits' end over you...
For that matter, Sarah herself deserves a mention. She mentions to Delbert that she's at the end of her rope and has tried everything she could think of. The pain she feels at not being able to help her son and fearing what will happen to him is clear in her voice and body language. It also resonates with anybody who has watched a loved one make poor decisions and can't do anything but watch.
The part where Silver encourages Jim after the boy thinks he has royally screwed up and caused the death of one of the crewmembers.
Silver: Now you listen to me, James Hawkins... ya got the makings of greatness in ya. But ya gotta take the helm and chart your own course! Stick to it, no matter the squalls! And when the time comes, ya get to really test the cut of your sails and show what you're made of... well, I hope I'm there... catching some o' the light comin' off ya that day..."
This was apparently a case of Write What You Know, as John Musker based it on a memory of his high school football coach giving him a particularly strong pep talk which ended with both of them in tears.
Jim's monologue right before Silver comforts him.
Don't you get it?! I screwed up! I mean, for two seconds, I thought maybe I could do something right!
Jim has his first open moment of emotional vulnerability after this conversation, unable to do anything at the end but rest his head on Silver's chest and start crying. Especially sweet/sad since Silver actually has to force himself to break off the hug he gives him a moment after. "Getting in too deep," indeed.
The look on Jim's face when he overhears Silver denying that he cares for Jim and is only pretending to keep Jim off of the pirates' tail...
Remember, Jim has felt this kind of pain before. He's been abandoned by his father because he didn't really care about him or his mother. And now, he's forced to go through that pain all over again.
When Silver sees Jim escaping with the map, he aims his laser cannon at him and has a clear shot... but finds himself unable to pull the trigger. You can actually see him trying to hike himself up to do it, and failing.
The scene where Silver leaves. The whole speech he gave about why he needs Jim to take Morph, when really he's talking about himself is emotional, then after a certain point both characters are sniffling and concealing tears right along with the audience. The part where Silver flies away to freedom and lets out the most joyful laugh ever is the final straw.
After the chewing out Jim gives Silver where he throws back Silver's words at him and tells him that he'll make sure Silver never sees one drubloon of his treasure, the two begin yelling at each other before Silver threatens to use the ship's cannons to blast him, Doppler, Amelia, and B.E.N. to kingdom come if Jim doesn't give him the map by tomorrow morning. He turns to leave until he notices Morph hovering beside Jim and orders him to "hop to it." When Morph remains beside Jim, Silver yells, "NOW!" at Morph, only succeeding in scaring Morph, who nervously hides behind Jim's shoulder. Silver and Jim then storm back to their respective bases, while Silver momentarily stops to look back regretfully.
The expression on Silver's face when Jim hurls the heartfelt speech Silver had delivered earlier about Jim's potential proves that he meant every word about Jim's potential and wanting to see the kind of man he would become. And now he threw it away. Ouch.
That look on Mr. Arrow's face as Scroop gleefully cuts his life-line. Poor guy...
Gets worst when Captain Amelia and the rest of the crew discover that Mr. Arrow "died in the storm because his lifeline [Jim's job] wasn't on tight". You can just see the anger and disappointment Captain has at Jim for "his negligence" that ended in her closes friend's death, especially when she complimented him not just five seconds ago. Her speech just shows us how much she's grieving, but she has to keep up a tough front for the crew.
A Blink-and-You-Miss-It moment, but when Scroop tells the crew that Arrow's death was because of Jim, the crew members glare at the boy. It's not just Amelia who's disappointed and angry with Jim, it's the whole crew (minus Silver, Delbert and Scroop.)
For a satisfying final image, Jim looks out to the stars, and sees an image of Silver in the clouds smiling down on him, complete with a star mimicking the gleam of his cyborg eye. Doubles as a Crowning Moment of Heartwarming.
Right after the "I'm Still Here" sequence, Jim asks Silver how he became a cyborg. Silver gets a sad look on his face and solemnly replies that "You give up a few things... chasing a dream" while looking at his mechanical hand. There's obviously a sad story as to what happened to him, one which the audience can only guess.