Here is the full list of all 54 Songs of Conquest achievements.
Win 25 times on non-campaign maps with Arleon
Win 25 times on non-campaign maps with Barya
Complete the last Loth campaign map on Hard difficulty
Win 25 times on non-campaign maps with Rana
Win 25 times on non-campaign maps with Loth
Complete the last Rana campaign map on Hard difficulty
Complete the last Arleon campaign map on Hard
Kill 100 000 enemies using ranged attacks
Kill 100 000 enemies using magic damage
Kill 100 000 enemies using melee attacks
Win 25 multiplayer (online or hotseat) games
Complete all Loth campaign maps (on any difficulty)
Win a battle using each of the official wielders
Kill three enemies using Breath of the Phoenix
Have ten or more Charged buffs on a troop
Have your troop die from a Quick retaliation
Have three or more Front Line Fighter buffs on a troop
Win siege battle as defender
Have troop perform six attacks on its turn
Cast each spell (over any number of games)
Make enemy kill his friend using Blind Hatred
Cast five Apocalypse spells on the same troop turn
Kill three enemies with one flame attack
Have enemy kill one of your own troops when you cast Blind Hatred
Use Dimensional Door to position your troop in three or more Zones of Control
Trigger three Attacks of Opportunity in a single Bull Rush
Burrow up next to three or more ranged enemy troops
Swap enemy troop into Acid Cloud
Block an enemy troop from burrowing up
Complete all Rana campaign maps (on any difficulty)
Kill three enemies using Chain Lightning
Use a teleport spell to get on top of or behind the walls in a town siege
Win four battles on the same turn with the same wielder
Win six battles in a row on the same turn
Use Repel to push an enemy troop into three Explosive Fungi
Win a battle with only a single one unit left
Kill three enemies with one sweeping attack
Win a battle without making an attack
Cast five spells on the same troop turn
Reach level 32 with a wielder
Max out town a town in a non-campaign game (tier 5, walls, upgraded buildings on all build sites)
Win a battle before the enemy gets a turn
Reach level 24 with a wielder
Win siege battle as attacker
Reclaim your town that is being occupied/razed/converted by the enemy
Win three battles on the same turn with the same wielder
Deal 500 damage or more in one attack
Complete all Arleon campaign maps (on any difficulty)
Have a wielder equipped with artifacts in all slots
Reach level 16 with a wielder
Reach level 8 with a wielder
Win two battles on the same turn with the same wielder
Complete all Barya campaign maps (on any difficulty)
Complete the last Barya campaign map on Hard difficulty