Here is the full list of all 30 Fishing: Barents Sea achievements.
Found port of Akkarfjord
Unlocked Sjarken
Catch 1,000 kg Haddock
Catch 1,000 kg Pollack
Catch 100 kg Redfish
Found port of Hammefest Centrum
Catch 100 kg Pollack
Catch 100 kg Haddock
Have a fish on your boat.
Catch 100 kg Cod
Catch 1,000 kg Cod
Catch 10,000 kg Cod
Catch 100 tons Cod
Catch 10,000 kg Pollack
Catch 100 tons Pollack
Catch 10,000 kg Haddock
Catch 100 tons Haddock
Catch 1,000 kg Red Fish
Catch 10,000 kg Red Fish
Catch 100 tons Red Fish
Catch 100 tons Mackerel
Catch 1,000 tons Mackerel
Unlocked Vibeke Cathrin
Unlocked Lunar Bow
Unlocked Hermes
Found port of Tufjord
Found port of Snefjord
Found port of Forsøl
Found Trawling Area
Found port of Rypefjord