Here is the full list of all 27 That's My Space achievements.
Get 500 points on Survival Mode
Gather 200 Iron Ores
Gather 500 Iron Ores
Gather 1000 Iron Ores
Destroy A Moon
Upgrade Anything To Level 5
Upgrade The Small Lasers To Level 5
Upgrade The Big Lasers To Level 5
Upgrade The Diagonal Lasers To Level 5
Upgrade The Laser Shotgun To Level 5
Upgrade The Rocket Launcher To Level 5
Upgrade The Booster Turbine To Level 5
Upgrade The Repair Bot To Level 5
Upgrade The Gravitation Field To Level 5
Craft Your First Chaotic Weapon
Craft Your First Cold Weapon
Kill 500 Enemies With Falcon In Survival Mode
Kill 500 Enemies With Galapagos In Survival Mode
Kill 500 Enemies With Crusader In Survival Mode
Kill 500 Enemies With Destroyer In Survival Mode
Kill 500 Enemies With Diamond In Survival Mode
Kill 500 Enemies With Marauder In Survival Mode
Kill 500 Enemies With Rogue In Survival Mode
Kill 500 Enemies With Scavenger In Survival Mode