Here is the full list of all 73 Planar Conquest achievements.
Make an alliance with another SL
Recruit The Last Uruthian
Have six max level heroes with all of their equipment slots filled
Recruit Aelys the Broken
Cast a spell with Ogre Mage
Cast a spell with Draylik
Win an encounter with army commanded by Bonebasher
Kill an enemy hero on the world map
Win as Alhasret
Win as Neve
Win as Magog
Win as Ariel
Win as Rastiss
Return from banishment
Build a city on water plane
Win as Istimaeth
Kill a Drake with a Settler unit
Have a hero reach maximum level
Have a unit deal fire, cold, electrical and acid damage with one attack
Achieve tier 9 in all elemental circles
Win as Drakhis
Win as Myrodants
Win as Prithvi Mata
Win as Orcs
Win as Erzsebet
Win as High Men
Win as Merlin
Win as Eyegor
Win as Grey Elves
Take control over every city on Air plane
Win as Dwarves
Win as Varkin
Win the game without casting any spells
Win as Markas
Win as R'jak
Win as Unhallowed
Visit earth plane by going through Earth Portal
Forge an artifact
Win by casting Spell of Domination
Win a game having spent (or gained) no points in SL creation
Win as Draconians
Research all available spells
Have a city of three living races
Summon a champion
Make a trade with another SL
Win as custom SL
Win the game by defeating all SLs
Win as Dark Elves
Travel to another plane
Defeat a SL
Banish an enemy SL
Raze a city
Construct all buildings in a city
Recruit a hero
Explore a world feature
Capture a city
Recruit a unit in one of your cities
Found a new city
Create a Custom SL
Enchant a unit with five unit enchantments
Research a spell
Cast a spell
Have at least 100k population in your empire
Reach 100 spellcraft
Win a battle
Reach 100 fame
Have a unit reach maximum level
Bless a Water Elemental
Conquer Hell Gateway feature
Conquer a city with army commanded by Vendral
Defend your city with army commanded by Kjorgi
Add Elven Hussar to your army
Reach maximum level with Nehanash