Here is the full list of all 13 Tails achievements.
Play a game of Zen
Play a game of Time Attack
Reach a score of 250 points in a game of Time Attack
Reach a score of 500 points in a game of Time Attack
Reach a score of 750 points in a game of Time Attack
Reach a score of 1000 points in a game of Time Attack
Evade 100 bombs overall in Time Attack
Collect 75 navigational powerups overall in Time Attack
Get 100 tail pieces in any mode
Get 250 tail pieces in any mode
Reach a combo of x7
Reach a combo of x15
Get 10000 points overall in Time Attack mode.