This is based on opinion. Please don't list it on a work's trope example list.
Tear Jerker / Beware the Batman
Alfred telling Bruce that he fears leaving Bruce alone would tug at the heartstrings of any father.
Tatsu revealing that her father died in a car crash when she was young.
The ink blots in Ravencroft's office remind Bruce of his parents lying dead in Crime Alley.
Magpie's whole backstory.
Magpie's whole everything.
Gordon's flashback of Humpty Dumpty's attack; you can see the pain in his eyes when he realizes that he failed to protect Humphry.
Barbara's delivery of this line after Jim's capture.
"He took him, Batman... He took my father..."
Humpty Dumpty's speech to Batman at the end:
"It's not my fault, Batman. I never really wanted to hurt anyone. Not like they hurt me. They dragged me into the middle of their war. Lt. Gordon, Tobias Whale, their war. I just wanted to go back to play with my numbers and my toys. But I can't. I can't go back."
While giving his speech, you can just hear the sadness in his voice as he break downs.
The fact that Humphry states that Batman is the best friend he has had in years.
It's sad how Humphry gives into insanity with this line.
"All the king's horses and all the king's men can't put Humphry Dumpler back together again."
Almost everything that Rex/Metamorpho goes through.
The look on Stagg's face when Sapphire runs away from him after finding out the truth.
"Wayne hooked. Awaiting instructions". This was after Bruce told Ravencroft that he's glad he's not her patient anymore.
Tatsu's reaction to seeing Alfred resigning from being Bruce's butler for betraying his trust and Bruce agreeing to his resignation and also firing her. Bruce doesn't really fire them, it was all part of his plan, but if this was real, then it would've be pretty sad.
Bruce: Why am I just hearing about this now? Alfred: It's not her fault, Bruce. Tatsu confided in me when she began working here. I kept her from you to protect her. She was just doing what she thought was right. But I betrayed your trust. Bruce: And... Alfred: And... I think the only appropriate solution is to tend to my resignation. Tatsu: (Gasp) Bruce: Accepted. Tatsu: (to Bruce) What?! No, you can't do that! Bruce: I accept your resignation as well, Ms. Yamashiro. And since I can no longer trust either of you, both of you will be gone by the time I get back.
The look on Bruce's face when Ravencroft betrays him.
Katana seeing Bruce shot and believing that he's dead.
The music that plays when Silver Monkey, having been outed as a traitor by Lady Shiva, is beaten to the floor by her henchmen (though he still manages to go down swinging).
Bethanie Ravencroft begging for forgiveness from Lady Shiva, only to have Shiva use the Soultaker Sword on her.
Batman acknowledging that what happened to Bethanie was his fault.
The music playing when Gordon looks at his daughter's room.
Gordon fears his job is to blame for Barbara's kidnapping.
Katana's reaction to seeing Jason being used as a puppet for Cypher
Cypher: A machine? No. I'm a man, just like you. Only upgraded.
An indirect one at the end. Right after Katana admitted she has feelings for Jason Burr, he is revealed to have remained under Cypher's control, possibly meaning the man she was beginning to fall in love with is lost forever.
Tatsu seals herself inside with the mutated ninjas to buy Batman enough time to escape.
Batman finding Katana in a near death state.
After Bruce shows off an impressive Sherlock Scan, we get this exchange:
Tatsu: When do you turn it off?
Bruce: I don't. I can't.
Batman's attempts to be kind and caring to Magpie fail, and instead causes her to develop a psychotic obsession with him that nearly gets Katana killed.
Magpie's heart breaks like six different times over the course of the episode. It's brutal. And it's made worse because there's a very real chance that Batman does care about her, but her insanity makes anything more than antagonistic relationship a non-starter.
The reason Batman visits Magpie at Blackgate: To see what could happen to him if he doesn't control his Batman persona, and how he's afraid he might be losing himself. The episode's ending clinches it.
A minor one, but Lunkhead relapsing and getting himself arrested, ruining his attempts to reform and later being manipulated and screwed over by Magpie.
Alfred's flashbacks throughout the episode that reveal how he lost Tatsu's father to the League of Assassins and a young, but traumatized, Bruce Wayne
The ending: Jason Burr falls victim to the Soultaker Sword right after regaining his mind, Batman is defeated and captured by Ra's al Ghul, Alfred and Katana barely escape from the League, and Ra's uses the Ion Cortex to plunge Gotham City into darkness.
Because that's apparently not enough, Tatsu also finds out what actually happened to her father at the worst possible time.
To follow up on that, Tatsu drawing her sword at Alfred and later even assaulting him when she believes Alfred killed her father.
This goes on for several episodes, but Bruce is clearly falling apart with Alfred gone. Tatsu has to walk out of a training session because he's pushing so hard that she's about to collapse.
Tatsu attempts to call Alfred at the end of the episode; you can hear the concern and worry in her voice full well.
Batman and Katana fail to stop Anarky from blowing up a park in the city.
Metamorpho has chosen a hideout that's within sight of Sapphire Stagg's home because he's unable to give her up entirely. And then it turns out that she's the mastermind behind Old Gotham's residents being terrorized. Darn good thing he (supposedly) didn't find out, eh?
Tatsu tries to help Rex think of a codename; his melancholy responses really just hammer home his depression.
Batman's No-Holds-Barred Beatdown of Killer Croc. It's his lowest point during Alfred's absence. It even freaks out the criminals watching.
His response when he realizes Katana is watching is heart-wrenching.
Batman: Go away... you shouldn't see this.
Kirk Langstrom was on the verge of curing several diseases with a serum developed from bats... and then Pyg and Toad turned him into a mutant freak forced to be their slave.