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