Sean's Ending in Street Fighter III: First Strike and Second Impact. Ken instructs Sean of the only training possible to beat him: By properly defeating Ryu.
In Jade Empire, it is possible to purchase some training techniques that the Big Bad's Lotus Assassin army uses. One such technique, Deadened Nerves, is apparently taught to a student by beating him until he no longer feels it. First knotted rope is used, then bamboo rods, and finally iron staffs. Not that any of this actually happens in-game...
Note that your character never goes through the indoctrination, general training or even gets the Lotus uniform... honestly, they need better quality control. Not surprisingly you get to betray them, free or kill their slaves and just wreak havoc. The villains are holding the Idiot Ball then...
The only reason The Kid from I Wanna Be the Guy had any chance of success is because he went through particularly harsh Training from Hell prior to the game's start, though the whole of I Wanna Be The Guy could be seen as the Training from Hell The Guy must go through, Klingon Promotion style.
And for those who play platformers, IWBTG is Training From PlatformHell.
In Phoenix Wright: Ace Attorney, spirit medium and Phoenix's sidekick Maya Fey searches for a freezing waterfall to stand under for eight hours as part of her training. After failed attempts with Phoenix's shower and the local fire station, one of the characters during the ending sequence says that Maya did find a freezing waterfall...and caught a cold.
Taken to an even greater extreme in Trials and Tribulations; the initial premise of the fifth case is a trip to a Hazakura Temple, a training temple for spirit mediums. One of the training courses Hazakura offers is the "Special Course," in which the trainee sits on a block of ice while being doused in "spirit water" and chanting a spell 30,000 times.
Also, a mini-manga released in Japan with the DS remake of the first game shows a training montage the night before Phoenix's first court case. If Phoenix gets so much as a small detail wrong, Mia hits him with a shinai so hard, it breaks. The title approximates as "Phoenix's Special Training From Hell".
It's subverted when you realize that it's training for bullet hells.
In order to cure herself of her crippling (and painful to watch) Fear of Thunder, Genki Girl Rikku from Final Fantasy X spent a solid week in the Thunder Plains, a region with endless rain and lethal thunderstorms that are barely kept in check by a few lightning rods here and there.
Truth in Television: G. Gordon Liddy, best known for his role in the Watergate scandal, also had astraphobia and cured it by climbing a tree during a severe thunderstorm.
No More Heroes has a rather vanilla "training" in Thunder Ryu's gym, which is just dumbbells, bench pressing and squats (although Thunder Ryu is kind of predatory...). But it also has training from Hell when you give Lovikov the Lovikov balls. Judging by the sound effects, he teaches Travis his techniques by beating the crap out of him.
EarthBound's Poo has to undergo "Mu Training" before he even joins the team, consisting of having his legs, arms, ears, eyes and mind broken by "the spirit of his ancient lineage."
An interesting inversion occurs in Breath of Fire III. This time, you aren't on the receiving end of the Training from Hell. You get to train nebbish, cowardly bookworm Beyd so that he can take on Zig. Meeting in the town square, training consists of ten rounds (or less) of beating Beyd silly in order to increase his core physical stats (HP, Defense, Strength). If the player is as obsessive about it as this guy always is (partly because he could never count on Zig to land a critical and spend a turn bragging so that he could heal Beyd), nebbish, cowardly bookworm Beyd becomes confident, Physical GodBadass Bookworm Beyd! (Seriously, if you train him enough, it's possible for him to wipe out Zig in one attack, as well as one party member per turn).
Inverted in The Misadventures of Tron Bonne where the player as Tron is the one putting the Servbots through their paces. The attack training consists of the Servbot catching live bombs and then throwing them back at cardboard cutouts of the game's citizens, the speed training is three days of kitchen duty where you have to serve meals to the other Servbots under increasingly harsh time limits, and slothfulness is cured in the torture room using spikes, flames, and a 10 ton weight.
Master Zen's training in Tony Hawk's American Wasteland; Even though you're pretty capable of winning AMJAM before you meet him, it's still necessary to learn his secrets. And, while the fact that you never see him on a skateboard himself might seem a little suspect, he's just a little nutty and forces you to Die or Fly by stalling on a freeway sign, facing certain death if you fall. He also sees if you are "strong of body" by having you hurl yourself into a wooden tower until it breaks, and tests your "mind" by making you bash through a roof with your head. Of course, his training has its benefits; No other skating instructor gives you freaking superpowers like the Special system or the strength of ten men, after all.
The Combat School mode in some Metal Slug games is like this; in Metal Slug 7, your "training" missions start out fairly simple, but playing through the main campaign unlocks a series of progressively more insane challenges, such as keeping balls in the air while being continuously attacked, jumping as much as possible while fighting off enemy troops, playing a game of Chicken with a giant sled, replaying the giant mech duel boss without your giant mech, trying to beat the final boss with no special weapons or extra lives as fast as possible, and fighting off a platoon of giant maneating plants with only a combat knife.
Corporate-run "Biotic Acclimation and Temperance training" is part of Kaidan Alenko's backstory in Mass Effect, and he describes it as Training from Hell: "you either came out a superman or a wreck. A lot of kids snapped. Some died." Operating in the early days of human biotics, before the study and training of them was regulated, BAaT involved rounding up teenagers who manifested biotic abilities and sending them to a barren space station at the edge of the solar system, with no access to the extranet, to be trained by turian (as in, "our enemies from the recent First Contact War") mercenaries. One of them, Commander Vyrnnus, liked to tell his students "I was at the helm of the dreadnought that killed your father," and his teaching methods included breaking one student's arm because she tried to get a drink of water without using her biotics.
And Kaidan got off light compared to the horrors that Jack went through in Mass Effect 2 at the hands of the sadistic Cerberus researchers at the Teltin facility on Pragia. It speaks volumes that forcing children to fight and kill each other was probably among one of the least evil things that went on there.
According to the codex, to even get into the N-Program, candidates have to train for 20 hours per day, leading small combat teams through hostile terrain, with little sleep or food. Even getting accepted for training in the N-Program earns a soldier massive respect, even if they wash out at N1 level. Anderson reveals that N1 training, for instance, has the recruit dropped on an asteroid with no navigation data, no radio equipment, no food or water and only a limited amount of oxygen, with no objective other than "survive". N2 through 5 get even worse, while N6 is conducted in active warzones. Out of the few who made it to N6, only those who've proven exceptional in the field, are finally awarded the coveted N7 designation. It goes without saying, Anderson and Shepard both graduated training with this rank.
The academy in Mario Tennis: Power Tour has training machines that allow senior and varsity players to gain experience for learning Power Shots. These include a treadmill run, where banana peels and barrels are tossed at you every few seconds; a devices where you spin around to collect coins while dodging jets of fire; and the "Duck Walk", an obstacle course where you mostly hop on one foot and try to avoid stepping on an electrified floor.
The "sumo robot" requires repeated tackles to destroy, and comes equipped with a rocket punch that knocks your character senseless if it's not defended against. The trope itself is lampshaded by the numerous NPCs (and a few coaches) in the training area who are seen either recovering from the training or wondering aloud how performing these tasks could possibly help their tennis play.
In Final Fantasy Tactics A2, the Goug Nightwatch (a gang of rather wimpy Moogles) beg your clan to "train" them. Said training obviously consists in beating the crap out of them.
It does pay off though, since they become stronger each time you continue the quest. And since they will all join you for another quest, it's worth to do it several times.
The live-action commercial for Halo 3: ODST depicts Tarkov and the other ODST trainees going through this.
The SPARTAN training is known to be even more grueling. The children — and they are children — are finished with standard military training before they're ten years old. Before they hit they teen years they're being trained with live fire simulations with trainers who are really trying to maim and kill them. They're instructed to do the same.
The ending of the first loop of DonPachi reveals that the events of the game were training for the DonPachi Squadron, an elite troop of super-soldiers. It's hellish both physically and emotionally, because the enemy is in reality the player's allies, who are all posing as the enemy in order to allow this training regimen to happen.
Although there's not a Training From Hell sequence per se, Final Fantasy VIII's Balamb Garden military academy has a "Training Center" which consists of an area where live monsters (including T-Rexes) roam. The Training Center is the only Garden facility open to students at all hours; the infirmary, meanwhile, closes at curfew. It's also worth noting that the prerequisite for Garden's final exam involves traveling to a monster-infested cave to do battle with an elemental spirit; the field exam itself involves squads of teenagers being turned loose on an actual battlefield.
In Final Fantasy XIII, Barthandelus sends the party to GranPulse to force them to become strong enough to kill Orphan — an act that would destroy Cocoon and everybody on it.
Level Grinding in any game is essentially the players forcing their characters to go through Training from Hell. A few hours of this will feel like hell for the player as well.
Inazuma Eleven: In the anime version, other than the daily push-ups, and practicing with tires, there are the Flash and Naniwa Training Facilities, which unlike in the games, they provide outright unnatural and painful training programs.
Marching Flame Scouts from Mousehunt are trained by getting chucked into the first wave of battle on the front lines to fight against deadly mousetraps. And they don't get any prior combat training or experience.
In Psychonauts, Raz states that back in the circus he lived in, his father made him go through training so rigorous that he came to believe that his father was secretly trying to kill him for being a psychic. As it turns out, Raz's dad was also a psychic whose training was to help him control his powers.
Saints Row The Third: Angel's training regimen includes things like being set on fire and going on a car ride with a tiger. The Boss is not amused.
In Knights of the Old Republic II, it's revealed near the end that Kreia had orchestrated most of the events in the game, as part of a complex ploy to lure the Exile back to Republic space, put them through hell and make them stronger for it... and it worked!
The evil shinobi of Senran Kagura go through this part of their regime. This is mostly to compensate for the fact that the evil shinobi will take anybody who strolls through the gate while good shinobi only take those who already have a significant measure of skill and training.