Here is the full list of all 35 Grey Goo achievements.
Feed a Mother Goo to a Proto-Purger (in any aspect of the game)
Win a one-on-one multiplayer match
During a multiplayer match, build the maximum possible number of units
Build an Epic unit
Win a skirmish match against an AI
Win a skirmish match against the AI with each of the factions
Win a skirmsh match against 3 AI opponents on hard difficulty
Win 100 skirmish matches
Win a 2v2 multiplayer match
Win a four player free-for-all match
Win 100 multiplayer matches of any size or mode
Complete the Beta campaign on any difficulty
Complete the Human campaign on any difficulty
Complete the Goo campaign on any difficulty
Complete all missions of the campaign on any difficulty
Complete all missions of the campaign on Hard difficulty
Win a multiplayer match after destroying an enemy Epic unit
Destroy each faction's Epic unit during a multiplayer or skirmish match
Build the Epic unit for each faction
Win a skirmish or multiplayer match in Total Annihilation mode
As Human or Beta, complete a multiplayer or skirmish match without ever hitting the resource cap
Win all missions and complete all bonus objectives in the Beta campaign on any difficulty
Win all missions and complete all bonus objectives in the Human campaign on any difficulty
Win all missions and complete all bonus objectives in the Goo campaign on any difficulty
Win all missions and complete all bonus objectives in the campaign on any difficulty
Win all missions and complete all bonus objectives in the campaign on hard difficulty
Have at least 3 of every Sentinel type in your base at once during a single ranked multiplayer match
Rebuild your HQ (in any aspect of the game)
Win a LAN match (against an actual person or persons)
Consume 100 enemy units or structures with formless Goo in a ranked multiplayer match
Destroy 5 Extractors or Mother Goos with a Mother Goo in a single ranked multiplayer match
Heal 1000 or more damage using the Repair Pad structure during a single ranked multiplayer match
Have at least 20 units mounted on wall pillars at the same time during a single ranked multiplayer match
Use the Teleporter structure at least 3 times and teleport at least 5 structures during a single ranked multiplayer match
Complete the Mago's Pass mission without losing a single civilian