Go to the dock area (with the jetty) in Onomichi to trigger a sub story involving a fisherman. Eventually he'll offer to take you spear fishing. This is a minigame where you throw a spear at fish to collect them. At the very end of the first level there is a giant squid boss which takes a lot of spears to kill. You'll get the trophy for killing it. I'm not sure if you can actually miss it or fail to kill the giant squid as I succeeded on my first try. Either way it definitely appears on the first spear fishing level.