Sonic Adventure

The longer way to do this is to beat Chaos 6 is Sonic's story, or finish Sand Hill as Tails.

Alternatively, if you talk to Big in the Adventure Field, you unlock him then also. The soonest you see him is right after you finish Ice Cap and right before you start Twinkle Park. You can find him in Station Square, in the area with the elevator to Twinkle Park. He'll be standing to the right of the dock. The achievement won't pop until you exit the game and go to the character select screen, and you'll get it the moment you do.

Happy hunting!

The fastest way to unlock Big the Cat is to finish the "Chaos 6" boss with Sonic the Hedgehog.
Also unlocks with Miles Tails Prower after the Sand Hill mini-game.

EDIT: Not sure if this is the right place to put it, but, oh well.

Here's a few things I've found out while going for the harder ranks:

1) Use the thumbstick to actually pull the fish so that it faces you. This will immensly help you when the fish are swimming away from you. Yes, it will still take long, but it'll be much faster than just waiting.

2) Don't use the B button. Slowly and rhythmically pressing the A button will work wonders.

3) The last one seems kind of obvious, but get as close to the fish as possible before casting.

Hope this helps.