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