Here is the full list of all 29 Super Bout: Champion's Tour achievements.
Won a match in Arcade mode
Win a round without getting hit
Win 2 rounds in a match without getting hit
Win a match without getting hit
Win a round in under 15 seconds
Win a round in under 10 seconds
Win a round in under 5 seconds
Land a 3 hit combo
Land a 5 hit combo
Land a 8 hit combo
Get 2,000,000 points in Arcade Mode
Get 2,750,000 points in Arcade Mode
Get 3,500,000 points in Arcade Mode
Complete Arcade Mode with Cowboy
Complete Arcade Mode with Headband
Complete Arcade Mode with Wrestler
Complete Arcade Mode with Monkey
Complete Arcade Mode with Crab
Complete Arcade Mode with Ninja
Complete Arcade Mode on Hard difficulty
Complete all Trials with Cowboy
Complete all Trials with Headband
Complete all Trials with Wrestler
Complete all Trials with Monkey
Complete all Trials with Crab
Complete all Trials with Ninja
Complete all Trials