Here is the full list of all 69 Hero Academy achievements.
Link a Medic to a Heavy.
Win 50 games with the Council.
Hit three enemy heroes or crystals at once with a single Gunner attack.
Have an Engineer equip three allies in a single turn.
Do 2000 or more damage with a single attack.
Do 2500 damage or more with a single Ninja attack.
Knock out two enemies at once with the Pyro.
Add Runemetal, Dragonscale, and Shining Helm to a single Knight.
Destroy two enemy crystals in a single turn.
Win a game by destroying the enemy's crystals.
Win 25 games.
Shield a crystal with an Engineer.
Win a game with the Dwarves.
Win a game and take no crystal damage.
Hit four enemy heroes or crystals at once with a single Grenadier attack.
Complete all Meet the Dwarves challenges.
Hit three enemies with a single attack by a Wizard with a scroll.
Take all day to put in your turn after your opponent does.
Complete all Meet the Shaolin challenges.
Hit three enemies at once with a Heavy's attack.
Get a Paladin to heal herself.
Win a game by destroying the enemy team.
Win a game against a random player.
Resurrect an opponent's Ninja, Wraith, Chieftain, or Annihilator with the Shadow.
Complete all Meet Team Fortress challenges.
Resurrect and fully heal a knocked-out ally in a single turn.
Submit 100 turns.
Attack a single enemy with three different heroes in one turn.
Knock out a full-health enemy with one shot from an Archer.
Debuff three enemies in one turn with a Poisoner.
Stomp two enemy heroes in one turn.
Hit an enemy target at maximum range with the Sniper.
Submit a turn less than three minutes after your opponent moves.
Knock out three enemy heroes in one turn.
Use an assault tile to do bonus crystal damage.
Hit three targets with a single Windblade attack.
Knock out an enemy.
Submit five turns.
Win a game with the Team Fortress team.
Lower an enemy's maximum health by 250 with a Monk.
Win a game with the Council.
Win a game with the Shaolin Team.
Complete all Meet the Dark Elves challenges.
Complete all Meet the Council challenges.
Use the undo feature and try something new.
Taunt an opponent.
Complete the Tutorial.
Win 100 games.
Win a game with the Dark Elves.
Pull an enemy off an assault tile with an Impaler.
Weaken three enemies with the priestess in a single turn.
Hit three enemies at once with a Void Monk's attack.
Raise two Phantoms in a single turn with a Necromancer.
Build up a max-health Wraith.
Win 50 games with the Dark Elves.
Knock out three enemies at once with an Annihilator shot.
Win 50 games with the Dwarves.
Win a game with the Tribe.
Execute two enemies in one turn with a Warrior.
Hit three full-strength enemies in one turn with an Axe Thrower.
Do 1000 points of damage with a corpse explosion.
Heal three allies with a chained Shaman heal.
Damage five targets with one Chieftain attack.
Win 50 games with the Tribe.
Win 50 games with the Team Fortress team.
Complete all Meet the Tribe challenges.
Win 50 games with the Shaolin Team.
Removed an enemy hero's buff and a friendly hero's debuff in the same turn with a Taoist.
Complete all Challenge Collection challenges.