Here is the full list of all 61 Hero's Hour achievements.
Encounter 95% of all spells
Win a game as Enclave (normal or harder)
Win a game without hiring a hero
Win a game as Horde (normal or harder)
Win a game as Wild (normal or harder)
Win a game without casting magic
Win a game as Decay (normal or harder)
Win a battle without taking casualties
Win a Hardcore difficulty game
Win a game as Earthen (normal or harder)
Defeat a near impossible enemy army
Win a game as Order (normal or harder)
Have a hero with an artifact in all equipment slots
Create an Idol
Win a 5+ player game
Win a 7-player game
Win a game as Arcane (normal or harder)
Save 500 creatures using infirmaries and hospitals in a single game
Enter combat against an enemy player with at least 2000 power worth of army
Achieve rank 5 in a hero skill
Fully develop a town
Use a Forlorn Cloister with your highest levelled hero
Win a Challenging difficulty game
Win a game as Lament (normal or harder)
Have a hero reach level 20
Win a game before week 3
Win a Normal difficulty game
Win an Easy difficulty game
Win a game as Pyre (normal or harder)
Have three artifacts in a set
Learn an adventure map spell at an Archmage Tribunal
Acquire a treasure elemental
Defeat a challenging enemy in battle using only elementals
Win a game in less than 15 minutes
Win a game in less than 30 minutes
Win a game without any artifacts
Complete a full artifact set
Recruit 666 Pyre units in one game
Defeat the red dragon in Skirmish mode
Defeat the ghost larvae in Skirmish mode
Defeat the black dragons in Skirmish mode
Acquire a dragon via Diplomacy
Have a hero reach level 30
Have 100000 gold
Win a game as Tide (normal or harder)
Win a game as Pillar (normal or harder)
Devour a Black Dragon
Convert a town to a faction you did not start as
Put 200 power worth of units to work at a Slave Pens
Bloodwarp a Hatchling into a Seraph
Control 10 overgrown mines
Enter combat with a hero that uses the most overpowered Rune
Have a hero with a sum of attack, defence, knowledge and spellpower above 100
Cast Shadowcasting while your hero has 50 or more spellpower
Win a game on Hardcore+ and with hamlet starting conditions
Find an obelisk treasure with just 1 clue
Win a game on the Patience map in less than 24 real-time hours
Encounter 95% of all rare creatures
Encounter 95% of all artifacts
Encounter 95% of all adventure buildings
Achieve 95% of all achievements