Here is the full list of all 36 Tatsu achievements.
Enter two dragons into the arena on the same turn
Block an entrance segment
Beat the AI on Easy
Beat the AI on Medium
Beat the AI on Hard
Beat the AI on Harder
Beat the AI on Hardest (Dragon Master)
Check out all his majesty
Win your first online match
Win 3 games in a row, online
Win 5 games in a row, online
Win 10 games in a row, online
Win 15 games in a row, online
Lose an online match
Beat a player who has the 'Dragon Master' achivement
Win your first game against a human opponent
Destroy two enemy dragons in one roll
Destroy two enemy Fire Dragons in one roll
Expel two dragons in one roll
Expel two Fire Dragons in one roll
Destroy or Expel a piece when entering from the Mat
Enter and then Destroy or Expel two dragons on the same turn
Do an Escape that moves six spaces, as a White Dragon
Destroy a Fire Dragon from twelve segments away
Cover both Fire Dragon recruitment segments, while your opponent has no Fire Dragons on the Arena or Mat
Recruit both Fire Dragons in one turn
Prevent your opponent from moving any of their Dragons around the Arena, missing a turn
Get all nine dragons onto the Arena
Lose a piece in one of the enemy's entrance areas
Win without recruiting any Fire Dragons
Win by Clearing the board
Win by destroying all Vine Dragons
Destroy seven dragons in one game
Win without destroying any dragons
Win the game with your last 3 dragons
Win without any of your dragons being destroyed