Here is the full list of all 31 Star Vikings Forever achievements.
Complete a Challenge mission
Complete a Daily Quest
Complete Act 1
Complete Act 2
Complete Act 3
Complete Act 4
Complete all Challenge missions
Clear all stages on all acts, including Mystery levels
Perform a 15-hit Combo
Perform a 20-hit Combo
Level up a Shooter viking to level 9
Level up a Tank viking to level 9
Level up a Sneaky viking to level 9
Level up a Valkyrie viking to level 9
Level up a Sniper viking to level 9
Level up a Berzerker viking to level 9
Get your first Hat
Get one of each Hat type
Get all the Ship Upgrades
Level up 5 vikings to level 9
Complete Trials of Valhalla rank 9
Equip your entire party with Hats
Complete Trials of Valhalla Rank 12
Equip your entire party with Rank 3 Hats or better
Complete Trials of Valhalla Rank 20
Level up 10 vikings to level 9
Choose one: Complete Trials of Valhalla Rank 24; Equip your entire party with Rank 5 Hats or better; Get a Rank 7 Hat.
Compete with at least 20 friends on the Leaderboard
Choose any two of the following: Complete Trials of Valhalla Rank 24; Equip your entire party with Rank 5 Hats or better; Get a Rank 7 Hat
Complete Trials of Valhalla Rank 25
Perform a 10-hit Combo