Here is the full list of all 13 Greed Corp achievements.
In the Pirate campaign, destroy an enemy island of at least 3 tiles by strategically placing a harvester
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
Earn a combination of credits, tiles and carrier as an elimination bonus, 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
Win a 4-player match by fighting all enemies one at a time, in Battle Mode against only Skilled or Expert computer players
Earn 9 titles
Complete the single player campaign
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
In the Empire campaign, win a match without using a carrier
Build enough armed cannons to cover all remaining tiles in the map, in Battle Mode against only Skilled or Expert computer players
Win a match without the time expiring in any turn, in Battle Mode against only Skilled or Expert computer players
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