Meet the required number of Moons to collect to have the amiibo costumes available to purchase at the Crazy Cap stores after completing the game. Note that some of the costumes listed can't be received with the help of amiibo at all.

Outfit	How to unlock
Bowser's Top Hat	Collect 420 Moons.
Bowser's Tuxedo	Collect 440 Moons.
Bridal Gown	Collect 480 Moons.
Bridal Veil	Collect 460 Moons.
Classic Cap	Reach Mushroom Kingdom.
Classic Suit	Reach Mushroom Kingdom.
Diddy Kong Hat	Collect 300 Moons.
Diddy Kong Suit	Collect 320 Moons.
Doctor Headwear	Collect 220 Moons.
Doctor Outfit	Collect 240 Moons.
Gold Mario Cap	Collect 500 Moons.
Gold Mario Suit	Collect 520 Moons.
Hakama	Collect 380 Moons. (Cannot be acquired with amiibo)
Invisibility Cap	Beat Darker Side. (Cannot be acquired with amiibo)
King's Crown	Defeat the Broodals on the Dark Side. (Cannot be acquired with amiibo)
King's Outfit	Defeat the Broodals on the Dark Side. (Cannot be acquired with amiibo)
Luigi Cap	Collect 160 Moons.
Luigi Suit	Collect 180 Moons.
Mario's Top Hat	Reach Moon Kingdom.
Mario's Tuxedo	Reach Moon Kingdom.
Metal Mario Cap	Collect 540 Moons.
Metal Mario Suit	Collect 560 Moons.
Skeleton Suit	Reach Mushroom Kingdom. (Cannot be acquired with amiibo)
Waluigi Cap	Collect 260 Moons.
Waluigi Suit	Collect 280 Moons.
Wario Cap	Collect 340 Moons.
Wario Suit	Collect 360 Moons.