Here is the full list of all 27 Playing History: Vikings achievements.
Choose 3 Aesir deities
Defeat Lothar in combat
Choose 3 Vanir deities
Complete chapter 5
Defeat Bjorn in combat a second time
Collect 100 % of all coins
Complete chapter 4
Choose Christianity as your religion
Beat Olaf in a sparring session
Do ALL chrono busts
Complete chapter 3
Find the sword. Again
Collect 5 hammers
Do 4 chrono busts
Complete chapter 2
Collect 50 % of all coins
Defeat Bjorn in combat
Beat Tjorvi in a sparring session
Reveal your feelings towards your loved one
Collect 1 hammer
Complete chapter 1
Collect 25 % of all coins
Do 1 chrono bust
Find the sword
Collect 10 % of all coins
Inspect 20 items or persons
Inspect an item or a person