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