Here is the full list of all 27 Oblivion's Edge achievements.
Collide with an enemy ship
Destroy 100 enemies
Loose all your lives on Normal
Deploy 100 mines
Deploy 500 mines
Deploy 1000 mines
Defeat the first miniboss in Survival Mode
Defeat the third miniboss in Survival Mode
Defeat the fourth miniboss in Survival Mode
Defeat the Mothership on Easy in Survival Mode
Defeat the Mothership on Normal in Survival Mode
Defeat the Mothership on Hard in Survival Mode
Destroy 750 enemies
Destroy 1500 enemies
Loose all your lives on Easy
Loose all your lives on Hard
Allow 100k people to escape
Allow 500k people to escape
Allow a million people to escape
Allow 5 million people to escape
Allow 10 million people to escape
Save the satellite on Easy in Defend mode
Save the satellite on Normal in Defend mode
Save the satellite on Hard in Defend mode
Use the speed boost ability 10 times
Use the speed boost ability 50 times
Use the speed boost ability 100 times