Here is the full list of all 31 Dragon Climax achievements.
Defeat 20 enemies
Defeat 50 enemies
Defeat 100 enemies
Defeat 150 enemies
Defeat 200 enemies
Defeat 300 enemies
Defeat 400 enemies
Eating 5 foods
Eating 10 foods
Eating 20 foods
Complete all lessons at the dojo
Kicks 10 times barrel bouncing against the wall
Cut 15 watermelons
Collect 1500 points in the job: Kunai's Lessons
Destroy 35 barrels in the job: Burrel Buster
Collect 800 points in the job: Pet Food Collection
Play "Asteroid Defender Turbo"
Kill 30 Spiders
Complete Stage 1
Complete Stage 2
Complete Stage 3
Complete Stage 4
Complete Stage 5
Complete Stage 6
Defeat the first boss in the Stage 7
Complete Stage 7
Save Aoki
Don't save Aoki
Complete Hardcore Mode
Unlock Art Gallery
Unlock Aoki's Diary