Here is the full list of all 13 Greed Corp achievements.
In the Empire campaign, win a match without using a carrier
Complete the single player campaign
In the Pirate campaign, destroy an enemy island of at least 3 tiles by strategically placing a harvester
Win a match in a snow map in either the campaign or in battle mode
In the Freemen campaign, destroy an enemy unit or building with a chain reaction
Win a 4-player match while only losing harvesters through a self-destruct and owning at least one in every turn, in Battle Mode against only Skilled or Expert computer players
Win a 4-player match by fighting all enemies one at a time, in Battle Mode against only Skilled or Expert computer players
Win a match before the supporting funds go up, in Battle Mode against only Skilled or Expert computer players
Earn a combination of credits, tiles and carrier as an elimination bonus, in Battle Mode against only Skilled or Expert computer players
Earn 9 titles
In the Cartel campaign, fire a shell you did not buy from a cannon you did not build at the enemy you captured it from
Win a match without the time expiring in any turn, in Battle Mode against only Skilled or Expert computer players
Build enough armed cannons to cover all remaining tiles in the map, in Battle Mode against only Skilled or Expert computer players