This Seeking Tech guide will show you how to easily get the Coliseum Champion trophy and achievement.
Use the following video as a reference:
For this to unlock, you need to win 30 consecutive fights in the gold class gauntlet at the Brilehaven Coliseum. This gauntlet will be made available after you beat all the Ranked League fights.
Afterwards, talk to the Tactiturn Receptionist and then select the gold gauntlet. You then need to win 30 fights in a row to get this trophy. I was able to do this easily at around level 70 with four Tycoons.
If you aren’t using Merchants or Tycoons, then you may need to manage your MP throughout the fights.