Yuzu is the boss fight of Essentia's Mind Dungeon. He has two phases.
The heal bot will provide constant heals to Yuzu, so it's advised to take them out first. They can't be defeated in a traditional sense, only taken out temporarily. Alex's Smooth Jazz or Essentia's Sleep Shot are both easy ways to take the heal bot out of the fight for a bit. It's preferable to do this as attacking would require multiple turns to take out the bot.
For Yuzu's special sword dodging minigame, you are able to enter one side of the screen and go out the other. Use this to your advantage, you can avoid the jumping challenges given quite easily.