0107 Hitmonchan

Counter is the best fast move for Hitmonchan, and benefits from STAB. Bullet Punch is suboptimal stat-wise and doesn't have any real use; it can cover Hitmonchan's weakness to Fairy-types, but you shouldn't be staying in for those fights anyways. 

Hitmonchan is a Fighting-type Pokemon, and this moveset helps with remembering that fact. Frequent use of Power-Up Punch solidifies Hitmonchan's role as a Fighting-type and could help snowball its way to victory if left unchecked, since subsequent attacks become even more threatening. The choice between the elemental punches is up to personal preference and varies greatly depending on the situation and matchups. In general, Ice Punch is the more popular choice as it provides the best coverage, but the others still have their uses.

Hitmonchan becomes more of a swiss army knife with this moveset, which threatens up to 10 different typings. Thanks to the January 31, 2019 update, all of the elemental punches have identical stats and therefore Hitmonchan doesn't need to shield bait. While the low energy cost (40) per punch is appealing, their relatively low base power (55) leaves much to be desired, as they have a disappointing 1.38 DPE (Damage Per Energy) and lack STAB.

Hitmonchan burst on to the scene in Boulder Cup and has continued to see use in other formats, including open Great League. With a diverse and powerful set of tools (AKA punches) available, Hitmonchan defines itself as a very flexible pick with coverage to meet the meta. That being said, the lack of bulk compared to its competitors holds Hitmonchan back, as does the fact that the meta can often make its punch type predictable. You would usually rather have Medicham or Machamp, but if you are looking for extra fighting support or if tournament rules limit your choices, Hitmonchan is a more than reasonable replacement.   

While it's not possible to have coverage against every possible opponent, Hitmonchan's diverse moveset can sometimes take opponents by surprise. However, a loss against Giratina is the most common frustration among pokemon in Ultra League, even if Hitmonchan is rocking Ice Punch, and the low bulk doesn't help against hard-hitting Registeel either.

Hitmonchan's punches aren't legendary enough for it to punch its way into Master League. Even with Ice Punch Hitmonchan still loses to the big dragons in this league, though it is able to snag a narrow win off Dialga in the one-shield scenario. That said, there are better choices, and lots of them.