How to Tranquilize Large Fish
All tranq lethal weapons work to tranq large fish (including sharks), however you won’t be able to harvest the sleeping fish (if it is large) without a drone. If you have one, then you can bring it fully intact to the surface by going near the fish and holding Y to summon the drone (you get limited uses, 1 at base, 3 at max upgrade). Otherwise you will have to kill the fish with the gun in order to harvest it.
I suggest the tranq shotgun (Axel), as it offers both significant firepower and also fires 3 shots per ammo, so essentially giving you 3 chances per ammo to tranq on hit. The downside of course being less capacity and having to be really close to hit, but its definitely worth it imo. Otherwise you could go for tranq rifle for mid-range and better capacity, or sniper for high safety with range.
Max hush dart apparently works on large fish at the end game but I haven’t bothered to upgrade it that much. I prefer having a method of tranq that doubles as offense/defense for predators, hence the tranq shotgun recommendation.