Assassin's Creed Valhalla

There are a total of 19 different types of fish in the game. To unlock this achievement, you need to catch one of each type with the fishing line, which is obtained by building the fishing hut in your settlement in England and then talking to the owner. Note that killing the fish the your bow or melee weapon does NOT count towards this achievement. Because of this, there isn't really any way to keep track ingame of which ones you've caught, unless you never kill any and never sell/trade any. In that case, you can check your inventory to see which ones you have. Also be aware that size doesn't matter for this achievement. Many fish can be either small, regular, or big. You only need to catch one of that fish, regardless of its size; you don't need to catch all three sizes of all fish.
 
An ingame listing of all of the fish and where to find them can be bought from the fishing hut in your settlement. There are three books (Fantastic Fishes and Where to Find Them) that you can buy for relatively cheap to see where to find all types of fish in the game. You'll have far more silver in the game than you'll ever need, so buying these books shouldn't be an issue. However, the locations of all the fish are extremely vague, so here is a more specific list of locations. This is where I located every fish in the game. Obviously there are many places to find each one, and you'll likely find some while trying to find others. I would also like to note that I found every fish by fishing from docks or a coast. At no point did I need to fish off of a boat in a river or out at sea.
 
Norway:

1. Hake - fish directly off the docks in Fornburg
2. Mackerel - same as above
3. Redfish - same as above
4. Arctic Char - fish off the docks of Alrekstad in Hordafylke, or more west along the coast

England:

1. Bream - fast travel to Folcanstan in southern Cent, and head west along the southern coast until you find some fish
2. Brown Trout - on the eastern side of Dudmasten Lake (southeast corner of Sciropescire)
3. Bullhead - fish off the docks of your settlement in England
4. Burbot - fast travel to Glowecestre, and fish in the river between there and Oxeneforda to the east
5. Cod - Note - I believe you get 5 cod from either enemies or part of a story quest or World Event, because there are multiple reports of people having 5 cod in their inventory and not needing to catch any for this achievement. If you want to catch one, fast travel to the Forward Camp in northeastern East Anglia and fish off the coast there
6. Eel - fish off the docks of your settlement
7. Flatfish - fast travel to Wulfaswic in southeastern Essexe and head east along the river, fishing as you find fish. I found flatfish as I got closer to where the river opens into the sea
8. Grey Trout - same as above
9. Haddock - fast travel to Mercian Tower in southeastern Lincolnscire, and head either slightly north or slightly west along the coast until you find fish
10. Halibut - fast travel to Grimsby in northeastern Lincolnscire, then head east along the river and look for fish
11. Perch - fish off the docks of your settlement
12. Pollock - you'll likely catch many of these while looking for the ones above, but the same spot as salmon below is a good spot
13. Salmon - fast travel to the southernmost viewpoint in Snotinghamscire, then head southwest to the river and fish there
14. Shad - same as Halibut above
15. Sturgeon - in Cent, fast travel to Saint Hadrian's Priory fast travel point, then head east to Rouecistre Fortress. Across the river to the west of the fortress are docks. Fish off these docks