Here is the full list of all 40 Expeditions: Viking achievements.
Recruit Morcant
Begin your first expedition
Spend a total of 300 skillpoints on any character
Clear out every occupied campsite in Denmark
Loot the passage grave in Skerninge
Commission the construction of a new longship
Complete the prologue
Get rid of the cult from Legacæstir
Bring the last of the druids to Perth
Intercept the meeting between Osred II and the Mercians
Escort Finnguala to Perth
Depose Osred II of Northumbria
Unify the Picts and the Gaels under King Caustantin
Drive the Northumbrian forces away from Hadrian's Wall
Drive the Pictish forces out of the mountain caves
Help Northumbria conquer the Picts
Help the Picts defeat Northumbria
Conquer Britain for the Norse and establish the Danelaw
Resolve your feud with Skule Skullcleaver
Complete the game on Medium difficulty or above
Complete the game on High difficulty or above
Complete the game on Highest Difficulty or above
Complete the game in Iron Man mode
Assume control of Orkneyjar
Fight alongside your father in the valley of Vigridr
Ravage all the monasteries
Recruit Aife
Complete Nefja's personal quest
Complete Ketill's personal quest
Become romantically involved with a member of your hird
Find all the cairns in Denmark
Find all the cairns in Britain
Find and destroy all the Christian shrines in the game
Clear out every occupied campsite in Britain
Equip all the pieces of the lost legionnaire's equipment
Reach Avalon
Complete all five bounty quests in Eoforwic
Uncover what became of your father's final expedition
Loot the treasure hidden in the sunken cave
Bring justice to the arsonist of Ribe