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