Here is the full list of all 58 Krosmaster Arena achievements.
Complete Frigost in Adventure mode
Complete Astrub in Adventure mode
Finish Incarnam
Open 10 Krosboxes
Open 100 Krosboxes
Open 500 Krosboxes
Recycle 10 Krosmasters
Recycle 100 Krosmasters
Recycle 500 Krosmasters
Obtain 10 Krosmasters from recycling
Obtain 100 Krosmasters from recycling
Obtain 500 Krosmasters from recycling
Win 10 ranked matches
Win 100 ranked matches
Win 500 ranked matches
Achieve 5 consecutive victories
Achieve 10 consecutive victories
Achieve 20 consecutive victories
Win 10 tournaments
Win 50 tournaments
Win 100 tournaments
Reach rank 15
Reach rank 10
Reach rank 5
Reach the elite rank
Collect 100 kamas during ranked matches
Collect 1000 kamas during ranked matches
Collect 10000 kamas during ranked matches
Win 3 ranked matches with a team made up entirely of Iops
Win 3 ranked matches with a team made up entirely of Sacriers
Win 3 ranked matches with a team made up entirely of Ecaflips
Win 3 ranked matches with a team made up entirely of Cras
Win 3 ranked matches with a team made up entirely of Rogues
Win 3 ranked matches with a team made up entirely of Srams
Win 3 ranked matches with a team made up entirely of Xelors
Win 3 ranked matches with a team made up entirely of Eliatropes
Win 3 ranked matches with a team made up entirely of Enutrofs
Win 3 ranked matches with a team made up entirely of Fecas
Win 3 ranked matches with a team made up entirely of Osamodas
Win 3 ranked matches with a team made up entirely of Foggernauts
Win 3 ranked matches with a team made up entirely of Pandawas
Win 3 ranked matches with a team made up entirely of Dreggons
Win 3 ranked matches with a team made up entirely of Bandits
Win 3 ranked matches with a team made up entirely of Knights
Win 3 ranked matches with a team made up entirely of Vigilantes
Win 3 ranked matches with a team made up entirely of Piwates
Win 3 ranked matches with a team made up entirely of Kanniballs
Win 3 ranked matches with a team made up entirely of members of the Brotherhood of the Tofu
Complete Brakmar in Adventure mode
Complete Moon Island in Adventure mode
Complete Forfut in Adventure mode
Complete Xelorium in Adventure mode
Complete Astrub in adventure mode with all available Krosmasters
Complete Frigost in adventure mode with all available Krosmasters
Complete Brakmar in adventure mode with all available Krosmasters
Complete Moon Island in adventure mode with all available Krosmasters
Complete Forfut in adventure mode with all available Krosmasters
Complete Xelorium in adventure mode with all available Krosmasters