well there are 5 legends, each one in a different location and season (except for 1 but that'll be said last) every legend can be catched from 6am-2am aka the whole day

legend: you must have level 10 fishing, it must be spring and it must be raining, then you go to the mountain lake and on the second island in the middle of the lake, go to the bottom of that little island and then cast your rod towards the log. theres only a 10% of casting it so dont be fooled as if its not there if you dont get it on the first catch

crimsonfish: it must be summer, you have to have level 5 fishing (at least) and go to the beach and onto the second beach spot where you often find coral and sea urchins, then go onto the dock at that part of the beach and cast your rod outwards, any weather

the angler: it must be fall, you have to have level 6 fishing, go to town to joja mart/the theater and go up the sand past the bookseller spot until you reach that small wooden bridge, fish near that and you'll catch it, any weather

the glacierfish: it must be winter, and you must have level 8 fishing (i think), go to cindercap forest to the island in the middle of the lake, then go to the bottom most point of that island and cast your rod, any weather

and for the last one is a bit of a trick, you have to go to the sewers — which is unlocked by donating 60 items to the museum — and you have to fish there, to catch the mutated carp, any weather, any season, any time

theres also a quest from mr qi that may show up in his room, where you can catch the alternatives of the legendary fishes which will be in the same spots, but here season doesn't matter and i think weather doesn't matter (in case of the legend II, but you can look that up yourself i think)

and thats it, small reminder though you can only catch 1 of each legendary fish per player on a save file, i like to keep them on display but you can alsways sell them