To do this select multiplayer from the menu. You then have the choice of joining a session (as I did), or creating your own. Once 25 fish are landed in that session you get the achievement. Joining a session in progress may give you enough time to complete this or it may not. For that reason unless you plan to fish a lot of multiplayer sessions then I would do this in your own hosted session.
The simplest way is to start your own session, you want 45 minutes or more to land the amount needed. Less and you not make 25 and have to start over.
When I joined a session it had 40 minutes left and I had the default tackle you get when starting the game. Had bought 0 items. I left my carp rod and float rod in the water and switched to them when they went off, but spent most of the time drawing a surface lure across the lake for predators, between the lure rod and the float rod I caught 25 fish with two minutes remaining. I had played for a total of 2 hours at that point and wasn’t very skilled.