Monster Hunters refer to the player-created avatars from Capcom's Monster Hunter series.
In every Monster Hunter game to date, as the game's title states, players take up quests in hunting and defeating monsters. The salvaged parts of defeated monsters can be used to create various pieces of equipment. Weapons, and the monsters whose parts can be used, vary from missions and the game.
The Hunter's Armor Set is a recurring set of armor throughout the Monster Hunter series. It is usually the first non-default armor available for purchase from the armory. The Hunter's Knife is the first sword and shield in the "Iron" series of weapons. The Rathalos Armor Set is also a recurring armor set. By repeatedly hunting Rathalos, a hunter can gather enough parts from carving to assemble the set. The set is modeled after Rathalos in appearance. The Blazing Falchion is a sword and shield that can be crafted from Rathalos parts.
Two Monster Hunter armor sets are the basis for paid downloadable content costumes for Mii Swordfighters. The armor sets used are the Hunter's Blademaster Armor while wielding the Hunter's Knife sword and shield set, and the Rathalos Blademaster Armor while wielding the Blazing Falchion sword and shield set.
The two Mii Swordfighter costumes from SSB4 were released as DLC for Ultimate on March 4th, 2021. The timing window for their release was set to double as a promotion for Monster Hunter Rise.
The trailer for the Monster Hunter costumes in Ultimate contain a myriad of references to the Monster Hunter series. Along with the Rathalos, the Hunter and Rathalos Equipment Miis are seen fighting several characters that refer to multiple monsters: a yellow Yoshi along with smaller Yoshis referencing Qurupeco, a bird wyvern that can summon smaller monsters to aid it in battle from Monster Hunter 3; pink Donkey Kong referencing Congagala, a gorilla-like Fanged Beast from Monster Hunter 2; Ridley referencing the Yian Garuga, an aggressive purple bird wyvern with noticeably hardened skin from Monster Hunter Freedom Unite; and a white Charizard along with many small white Kirbys referencing Khezu, a strange worm-like flying wyvern that dwells in caves and creates small larvae, introduced in the original Monster Hunter.
The Hunter Equipment Miis can also be seen performing Stone Scabbard and Blade Counter, which very likely serve as references to the long sword moves Spirit Helm Breaker and Foresight Slash, respectively. Similarly, the Rathalos Equipment Miis perform a parry, Hero's Spin, and Blurring Blade, likely referring to guard points, Amped Elemental Discharge, and Super Amped Elemental Discharge, respectively, which are all notable moves utilized by the charge blade weapon. Near the end of the Round 9 Mii Costume trailer, the hunter Miis are seen standing next to a collapsed Rathalos while a Mii wearing the Felyne hat is carrying a barrel. This is referring to hunters placing down barrel bombs on sleeping monsters.
Purchasing the Hunter's Mail costume alters the Palamute spirit battle introduced in the MONSTER HUNTER RISE spirit event, with the Mii Swordfighter in said battle switching to said costume instead of the Ninja Headband and Ninja Suit. Similarly, purchasing the Rathalos Armor costume alters the Razewing Ratha spirit battle which was added in version 13.0.0, with the Mii Swordfighter in said battle switching to said costume instead of the Ninja Headband and Standard Outfit.