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