The biggest issue I have with the octopus is that they just don't bite! The Glacierfish is the most difficult to reel in for me, but at least it takes the bait so I can try a couple times.
I've gotten Master Angler six times and each time, I caught the octopus on the submarine tour during the Winter Festival. I have never even hooked one on the beach. I usually have the trap bobber equipped, but I have also caught it with the lead bobber. I've used standard, wild, and deluxe bait. I always have level ten fishing when I've caught it.
Outside of the Glacierfish and Lava Eel, I'm terrible at rembering to use food to increase my fishing skill. If you can remember, make it easier on yourself by eating a dish o' the sea or an escargot or something before trying. I really need to put signs by my fishing spots or something...