This may be the hardest achievement in the game. Botfish can only be caught on the Arcadian Ruins, which is the last island you need to get to for the main story line. If you fish at the ruins you'll easily get a botfish to grab the line (not necessarily every time, but I probably hooked one 90% of the time).
The problem is actually catching it. The botfish will not only swim wildly back and forth but will occasionally zap the line with electricity, costing you half a heart. Sometimes it is simply impossible to catch it before you'll die. Some things that make it easier:
(1) Make sure you've got a lot of extra hearts: at least 8 or 9 will help
(2) If you keep trying and failing in the same place, try fishing from another location on the island. For some reason this often seems to make a big difference. I tried a dozen times around the pier where you land, with no success (often without having even knocked half the fish's strength away, although once or twice having him down to 5-10%). I then moved to the interior courtyard, down to the little sandy area and cast a line with me feet a bit in the water (took awhile to find a place it would let me). Caught the botfish on my first try from there.
A lot of this one is luck. You need to get a fish that likes pulling a lot in one direction (so you can tire it out) rather than one that keeps zipping back and forth and healing too quickly.