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