Here is the full list of all 18 Z Steel Soldiers achievements.
Complete Level 1
Kill 10 Psychos
Complete the Tutorial
Complete World 1
Complete World 2
Complete World 3
Complete World 4
Complete World 5
Complete World 6
Claim 25 Flags
Claim 250 Flags
Visit the Credits Screen
Kill 100 Ground Units
Repair 20 Bridges
Kill a Spy
Take over 50 enemy structures with Technician
Use a construction robot to build every type of building
Plant a virus in an enemy building