Here is the full list of all 48 Impire achievements.
Finish the Chapter 4 siding with Oscar in campaign mode
Finish every secondary quests in Chapter 4 of the campaign mode
Kill every boss
Have heroes trigger every type of single wall traps
Use the Lightning spell 250 times
Unlock 23 Runes
Finish the Chapter 3 in campaign mode
Finish every secondary quests in Chapter 3 of the campaign mode
Upgrade a squad to it's maximum potential
Craft every possible items
Finish the Chapter 2 in campaign mode
Kill 1000 Heroes
Raid 300 sites
Earn 50 Tech points through the use of rooms
Raise your dungeon up to level 10
Have heroes trigger every type of double wall traps
Have heroes trigger every type of ground traps
Earn a free unit
Finish the Chapter 1 in campaign mode
Finish every secondary quests in Chapter 1 of the campaign mode
Raid 150 sites
Kill 100 Heroes
Raid 50 sites
Raid 15 sites in a single mission
Complete a mission without Baal dying
Unlock 46 Runes
Kill 5000 Heroes
Ransom 100 heroes using the Prison.
Summon every single Fiend unit
Summon every single Souless unit
Get 50 Heroes drunk
Blow up 100 units
Finish the Chapter 4 siding with Velvet in campaign mode
Finish every secondary quests in Chapter 2 of the campaign mode
Finish every missions of the Campaign mode in Co-Op
Win a mission of the Campaign mode in Co-Op
Win a mission of the Campaign mode in Co-Op with 3 other people
Complete every missions of the Campaign mode without Baal dying
Win a multiplayer skirmish game
Win a multiplayer skirmish game in Capture the Dragon mode
Win a multiplayer skirmish game in King of the Hill mode
Raise your dungeon lord to lvl 10 in a skirmish game
Kill 10 opponents' dungeon lord
Kill 100 opponents' dungeon lord
Kill 500 opponents' dungeon lord
Kill 5 dungeon lord in a single skirmish game
Win a multiplayer skirmish game without your dungeon lord dying
Win 25 multiplayer skirmish games without your dungeon lord dying