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