Just wait till you're either right on top of the shadow or very close to it, and then dive down and you should be able to swim fast enough to catch it. Just keep pressing "A" I believe.
I can't do it. I really can't catch one. I've been trying for an hour and half. I just can't. I'm so upset. I can't believe I won't be able to complete the festival.
Hey, try catching it on the island.. the waters are much wider there so there's more swim time for you to chase it.. and I believe lobsters are more common in the island, probably the most common big shadow there is... when I tried diving for it in my town, mostly i got red king crabs, but when I went on the island, the first big shadow I caught was a lobster... It's a big shadow that moves, if it's a big shadow and doesn't move, that's most likely a seaweed
Try save and continue. Than try leaving the game without saving. You'll have to listen to resetti but Franklin might give you a new recipe.
If you do get a new recipe and get everything do the save/continue before you give the items to Franklin. If the next recipe is a hard one than leave the game without saving. You should get another recipe.
Try the island, I got a lobster in less than 5 minutes... if you're not good at diving, then just keep on doing it... it gets easier chasing the moving diving shadows once in a while.. I don't perfectly time my dives, but the island has good water space so I get a pretty good chance to chase the shadow
I agree with the advice about trying the island, it's easier to dive there since there's more water so more animals are spawned and you have more room to chase them before they reach the floating barriers. You can also get a tutorial from Tortimer to practice your diving skills if you take the easy diving tour.