Every single Pokemon in this gym is a pure Ice-type. This means they all have weaknesses to Fire, Fighting, Rock, and Steel while only having resistance to Ice.
Talk to the guy at the beginning of the gym for a Fresh Water. Walk north onto the ice and you will slide into a curved bumper that will spin you southwest onto a blue square. Walk east and battle the Black Belt.
Standing in front of Battle Girl Mikiko, walk south onto the ice. You will slide into the bumper and stop. Walk east to land on normal ground. Walk south around the rock and west into the bumper. It will shoot you southeast onto a blue square. Walk north to slide onto the switch and rotate the bumper. Walk north to slide into a rock and then walk west to be in front of Battle Girl Mikiko again. Stand on the pointed square west of Mikiko and walk south to slide into the bumper. It will shoot you northwest. Walk west up the stairs and onto the ice. You will go over a ramp and land near another Battle Girl.
Walk west onto the ice and then north into the bumper. From the blue square, walk east, north, and east again into the bumper. Walk north to slide onto the path of four squares. Continue north onto the ice to slide near a Black Belt.
Walk onto the switch to the northeast. Continue east onto the pointed square and walk south into the bumper. From the blue square, walk west into the rock, south, and west into the bumper. Walk north once you land on the last blue square. Head southwest up the stairs to find Brycen. His Beartic has Icicle Crash, a powerful physical move that deals damage and has a 30% chance of making your Pokemon flinch.
Brycen awards you the Freeze Badge for defeating him. He also gives you TM 79 Frost Breath. It is an attack that will always result in a critical hit. Walk down the stairs and west to the ice path for a quick exit. Cheren and Bianca will be waiting outside. Brycen shows up and the Shadow Triad reveal themselves. They say Ghetsis and N are waiting for you in the Dragonspiral Tower. After the Shadow Triad disappear, Brycen and Cheren go north to the Dragonspiral Tower.
Items in Icirrus City Gym:
Received from the white-haired guy at the beginning of the gym.