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