Here is the full list of all 9 Algebra Ridge achievements. It takes around 0-1 hour to unlock all of the achievements on Windows.
Finish story mode with no upgrades at all.
Find the secret message hidden within the disk.
Complete the final chapter in story mode.
Finish story mode with a total score of at least 7500.
Complete the fourth chapter in story mode.
Complete the third chapter in story mode.
Land 200 hits within 30 seconds.
Complete the second chapter in story mode.
Complete the first chapter in story mode.