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