Here is the full list of all 18 Dino Galaxy Tennis achievements.
Finish first mission
Play as a legend
Finish story mode
Return a special attack
Return a super attack
Score 700 points in Armageddon challenge
Score 700 points in Endless challenge
Score 500 points in Flying challenge
Win badge on D-Earth
Win badge on Techstar
Defeat the robot
Defeat the robot after its upgrades
Ultimately defeat Doctor X
Score 75 points in Block Breaker challenge
Win against fully developed robot without losing health
Win badge on Wormzone
Win badge on TentaWorld
Win badge on Syberion