In Tri you could only get Fearsome Maw for breaking Gigginox's head. At least in low rank. In P3rd you could also get it from a shiny drop and as a capture reward. The Bradygames guide lists the same statistics as P3rd, but is largely based ont he Japanese guide of that game. Can anyone confirm it as a reward from either of those two other sources?
You can get a fearsome maw low rank for breaking the face. It's not a shiny drop but can appear in the rewards once you finish the mission. It's a super low drop chance though, I would recommend running in the guild hall for better results.
Note: You can break his face with both impact and cutting weapons. I did it with DS.