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