Fullmetal Alchemist's main characters managed to deal with these problems and push through.
5 The Fall of Xerxes
Xerxes was the home of the man who would come to be known as Hohenheim, AKA the Elrics' father. At the time, he was a slave who was tasked with caring for the first Homunculus, created by a royal alchemist. The King of Xerxes hoped to use the Homunculus' knowledge to become immortal, but the Homunculus tricked him, getting the King to create a transmutation circle around the entire Kingdom with himself and Hohenheim at the center. When the transmutation circle is activated, Hohenheim and the Homunculus are granted eternal life-at the expense of everyone else in the Kingdom. Hohenheim is horrified but powerless to do anything about it.
Unlike a lot of the moments on this list, Hohenheim wasn't able to power through; he's spent his life since guilty and depressed, while still struggling against the Homunculus (now known as Father) in whatever ways he can. The most peace Hohenheim ever obtained was probably when he was with Trisha Elric, the boys' mother. Even that respite couldn't last forever, though, and Hohenheim was forced to leave his new family behind.
4 The Elrics' Attempt to Revive Their Mother
One of the earliest moments in the series is also one of its darkest. Edward Elric, having lost his mother to illness, decides that he and his brother Al can use their alchemy knowledge to bring her back. While foolish, it's important to that Edward is literally a child, almost incapable of the kind of forward-thinking needed to recognize the danger here. The boys do their research and create the transmutation circle, as well as obtain all the chemical ingredients, but when they activate it, something horrible happens. Alphonse is consumed entirely by a mysterious force, while Edward loses his leg. He then awakes to find an inhuman abomination instead of his mother and is forced to sacrifice his right arm in order to retrieve Al's soul from the Gate of Truth.
The entire episode has a foreboding aspect to it, as it's told in flashback, so it's already apparent to viewers that this isn't going to go well. Every decision the boys make that leads them to their fate has the audience crying out to stop it, and then when the inevitable occurs, the scene is absolutely gut-wrenching. Ed was able to recover from this only because he retrieved Al; had he not, he'd have likely bled out on the floor, leaving a terrible scene for the Rockbells to discover. This is the moment that solidifies the bond between brothers and becomes the foundation for everything they will do afterward.
3 The Death of Major Hughes
Major Maes Hughes was one of the first people to take a shine to the Elric brothers, treating them warmly as if they were his own children. Hughes was a good man who loved his family a lot, especially his daughter Elicia. The Major had the misfortune of uncovering the homunculi ruling over the nation of Amestris, which immediately made him a target to them. While Hughes did his best to get out and get this information to Colonel Roy Mustang, he was ultimately murdered in cold blood by the sin/homunculus Envy, who took the extra cruel step of transforming into his wife before killing him, causing him to hesitate to retaliate.
Hughes himself, obviously, wasn't able to make a rebound from death, but his fall was a hard blow to everyone, from Colonel Mustang to the Elrics. Roy Mustang blamed himself heavily, as he felt his orders to Hughes were a big part of what led to his death. This culminates in the "terrible day for rain" funeral scene, where Roy dedicates himself to finding Hughes' killer, which is how he managed to pull through. When he does find out the truth on the Promised Day, he performs a brutal beatdown on Envy, but is ultimately robbed of vengeance when Envy destroys its own Philosopher's Stone.
2 Devoured by Gluttony
While Ed and Ling are battling Envy, all three are devoured by Gluttony, although it wasn't exactly intentional. Gluttony's stomach actually leads to another dimension, and so far as anyone knows, it's absolutely impossible to escape from. Trapped with an injured Ling and a very angry Envy, Edward could easily have been at his most hopeless at that moment and for that matter, Al, too.
Ed's brilliance and knowledge of alchemy were his saving grace here. He was able to put together a plan to escape once he saw the Philosopher's Stone that acted as Envy's core, and Envy was at least rational enough to agree to work together for its own survival. The plan, which involved opening Gluttony's false Gate of Truth, was the kind of thing that only Ed could've come up with, because only he had sufficient knowledge of the Gate to do it. Al also played a critical role here, managing Gluttony while the three were trapped inside.
1 The Fate of Nina
Renowned by fans as one of the saddest moments in all anime history, the episodes involving Nina Tucker are notorious, and this tragedy happens early enough that it really hammers home how dark Fullmetal Alchemist is willing to get. Being housed and mentored by the "Sewing Life" Alchemist, Shou Tucker, the Elrics' bonded with him and his daughter like family. Shou Tucker was being faced with a test to maintain his Alchemy Certification, though, and his research had stalled. Instead of dealing with this like a normal scientist, Shou went absolutely mad and used his own daughter Nina and their pet dog to create a chimera by fusing the two together. Ed and Al are horrified, but not as horrified as they are when they find her later, after the hybrid being has been killed by Scar, who saw it as a mercy.
Nina's fate encapsulates a lot of what makes Fullmetal Alchemist's dark moments stand out and be ed by fans. It's a betrayal of trust, in that Ed and Al thought Shou Tucker was a respectable man; it's an affront to nature, a big theme in the series; it's tragic, because Nina and Alexander were so sweet and innocent; and it's all fueled by nothing more than ambition, ultimately benefiting no one at all. Fullmetal Alchemist: Brotherhood makes its characters go through some really dark moments, but ultimately they come out on top by carrying the pain of these moment with them throughout the series.