Hitmonchan can be obtained as a gift for beating the Karate King in the Fighting Dojo in Saffron City. You can obtain either Hitmonlee or Hitmonchan in this manner, but not both.
WHAT ARE YOU DOING. WHAT ARE YOU DOING. STOP NOW. STOP. GO AWAY. SCROLL UP. YOU DON'T WANT TO DO THIS TO YOURSELF. YOU WANT HITMONLEE. NOT HITMONCHAN. NO. SCROLL. BACK. UP.
...Very well. I guess you're hellbent on picking the difficult route, then. Hitmonchan is more physically defensive than his brother, but sacrifices a bit of Attack and Speed in the process. Oh, and a lot of useful moves, too. In exchange for what? Elemental punches? Get out of here, this isn't the Sinnoh generation, you can't walk in here with that stuff combined with a Special Attack of 35. If you haven't guessed, Hitmonchan really has nothing to offer compared to the other Hitmon. But can you blame him? Yes you can, actually. And you will be blamed for not picking Hitmonlee instead.
Gym #5 - Koga (Fuchsia City, Poison-type): You don't really want to do this. Koffings are tough as nails, and Weezing is the king of nails. Muk might be easy if you get a hit in before it starts to set up its defenses and do similar trolly things.
Rival (Silph Co.): Um... Yeah. It's not going to be easy here. Hitmonchan is a bit weaker than Hitmonlee, and it definitely shows. Pretty much the only things you can hope to take out here are Alakazam and Blastoise, since Alakazam's only offensive move is Future Sight and it hits typelessly in this generation; the rest have some sort of issue about them preventing you from hitting hard enough. Gyarados and Growlithe have Intimidate, Exeggcute has a decent Defense stat combined with resistance, so you can only really beat it with Mega Kick if you went back and grabbed it from the tutor, Charizard knows Wing Attack, Blastoise is pretty defensive (again, only do if you have Mega Kick) and Venusaur can and will stall your nads off.
Giovanni (Silph Co., Ground-type): Rhyhorn is a no-brainer, so is Kangaskhan. After all, if you have a Fighting-type, why not use it? Nidorino doesn't have any stats, so neutral smack it if you want to.
Gym #6 - Sabrina (Saffron City, Psychic-type): Let's not. Let's just not. There are better ways to handle this. For example, not being a kamikaze.
Gym #7 - Blaine (Cinnabar Island, Fire-type): Dogs have Intimidate, horses have Bounce. If horses use Bounce, you can try Sky Uppercut, It's not safe, but it's doable.
Gym #8 - Giovanni (Viridian City, Ground-type): Remind me why Giovanni didn't evolve his Rhyhorns. Dugtrio shouldn't be too much of a problem either. Others are dangerous members of society and are best left to professionals.
Rival (Route 22, pre-Elite Four): Repeat of the last battle, except replace Alakazam with Rhyhorn in terms of how easy taking it out is going to be. Alakazam is now extremely scary. It has Psychic.
Elite Four Lorelei (Indigo Plateau, Ice-type): Dewgong and Lapras shouldn't be too problematic. Jynx will be, I guarantee you this. So will Slowbro. Cloyster isn't dangerous since it hits with Dive, if you know when to use your attacks, like you should!
Elite Four Bruno (Indigo Plateau, Fighting-type): What the heck is an Onix? The rest you shouldn't bother with. Maybe Bruno's Hitmonchan. Maybe. Yours will most likely be higher level than his.
Elite Four Agatha (Indigo Plateau, Poison-type): If you have even a semblance of a brain, you'll know why this is a terribad idea. Unless you picked up Rock Slide, you have no way of dealing with any of Agatha's mons.
Elite Four Lance (Indigo Plateau, Dragon-type): Dragonairs should be easy (doesn't mean they will). The others have some sort of issue that will make them difficult, mostly about resisting Fighting moves.
Champion Rival (Indigo Plateau): Same thing as last time. Pretty much exactly the same thing as last time. Except his entire team is fully evolved. No types have changed, and no difficulty levels have increased, really. Or decreased. Exeggutor is maybe safe, since he left his Psychic-type attacks in the car. The others are just reruns of previous battles with the rival.
You'll want Sky Uppercut (level 32). It's really the best thing you can hit anything with. Mach Punch is useful too. Don't even bother with the elemental punches. What do you think this is, the post-split era? You'll also want to grab either Mega Punch (level 38 or Route 4 Move Tutor), Mega Kick (which trades a lot of accuracy for a LOT of power) or Strength. The last move is either Earthquake or Rock Slide, and it's a good thing you can't have both because either is a waste on Hitmonchan. Then again, if you really want trash like this on your team, better beef it up with anything you can get your hands on.
Recommended moveset: Sky Uppercut / Brick Break, Mega Kick / Double-Edge / Return, and any two between Rock Slide / Bulk Up / Mach Punch / Earthquake
Minimum stats are calculated with 0 EVs, IVs of 0, and a hindering nature, if applicable.
Maximum stats are calculated with 252 EVs, IVs of 31, and a helpful nature, if applicable.
What Nature do I want? Adamant, Jolly, not Modest, not Timid, pretty much the standard Fighting-type dealio. To add to that, Careful is useful, as it makes you bulkier for the price of losing little.
How good is Hitmonchan in a Nuzlocke? It's not. It's just not good in a Nuzlocke. Better Fighting types exist, it doesn't have much in terms of move options, and it doesn't have outstanding stats. Plus, Fighting-types are already pretty obsolete by the time you get to use a Hitmonchan anyway, so what's even the point? If you really want to sacrifice your Lapras for one of the Hitmons, waste it on Hitmonlee. It's way more worth using than this.