A simple offensive set is the best way to utilize Hitmonchan. Although it might not look very unique at first, access to Iron Fist, a plethora of punching moves that get boosted by said ability, and priority in Mach Punch give it all the advantages that it needs and somewhat make up for its inferior power. Without Psychic- and Ghost-types, Hitmonchan is surprisingly difficult to wall, so it can serve as an effective wallbreaker with its good coverage while keeping faster Pokemon in check with Mach Punch. Drain Punch is the preferred STAB option, as it gets boosted by Iron Fist, making it reach decent levels of power while simultaneously healing off damage taken from Life Orb. Alternatively, Close Combat can be used, as even factoring in Iron Fist it is stronger than Drain Punch. Mach Punch is an important move for Hitmonchan, as it is one of the few Pokemon that can learn the move, allowing it to finish off or revenge kill foes weak to it; for example, it almost always OHKOes Sawsbuck and Crawdaunt after Stealth Rock damage. Thunder Punch allows Hitmonchan to 2HKO bulky Water-types, such as Poliwrath and Slowking, and it can also hit Flying-types hard on the switch. Ice Punch is preferred for the final slot, getting good coverage with Thunder Punch to form a pseudo BoltBeam combination and hitting Pokemon such as Tangrowth, Druddigon, and Amoonguss for super effective damage. However, Hitmonchan could instead use Rapid Spin in this slot, as it allows Hitmonchan to rid the field of hazards, though this is at the expense of losing coverage. Keep in mind though that it loses to all relevant spinblockers, so only use it in case space cannot be made on your team for the few other Rapid Spin users in the tier and Hitmonchan's other traits are needed.
Hitmonchan should always run maximum Attack and Speed with an Adamant nature, as it needs all the power it can get and needs to outpace Absol, as Mach Punch will then make Sucker Punch fail, which can do a lot of damage despite the resistance it has. A Life Orb is preferred simply because it offers more power, and Drain Punch mitigates the recoil damage from the item anyways. Fire Punch can be used over one of Hitmonchan's coverage moves, and is notable for getting past Bug-types such as Escavalier and Galvantula, but space is fairly limited on this set and Fire Punch doesn't offer as much offensive coverage as the other moves that Hitmonchan typically uses.
Like almost every other Fighting-type in the metagame, Hitmonchan struggles a lot against Ghost- and Psychic-type Pokemon, having nothing in its movepool that can be used to defeat them reliably. Due to this, Pursuit support from the likes of Absol, Spiritomb, and Escavalier is a good idea, as it can trap them or hit them with a stronger move if they decide to stay in. In addition, if Ghost-types are eliminated, Hitmonchan can use Rapid Spin more freely. If Hitmonchan is running Rapid Spin, Fire-types, such as Moltres and Entei, also make good partners, as they appreciate the lack of entry hazards on the field and can switch into Will-O-Wisps from the Ghost-types that carry them. They also offer the ability to destroy said Ghost-types as well as the Bug-types that resist Hitmonchan's STAB moves. Hitmonchan is easily taken out by STAB Flying-type moves from the likes of Moltres and Sigilyph, making Lanturn a good partner since it resists Flying and has the bulk to take all their other moves, while Heal Bell can cure Hitmonchan of troubling statuses, most of which severely cripple Hitmonchan. Although Archeops stands a chance at beating Lanturn with Earthquake, Hitmonchan can hit Archeops hard with any of its moves, so the likelihood of one directly threatening Hitmonchan is rare.