To unlock Big Game Hunter achievement or trophy in Final Fantasy 13-2, you need to defeat every worthy opponent in the game. There are four worthy opponents that are located in Archylte Steppe. They are all associated with their respective Fragments:
It spawns in the southeast section of the map when weather is cloudy.
It spawns in the east section of the map when weather is sunny.
It spawns in the west section of the map when weather is rainy.
It spawns in the southeast section of the map when weather is thundery.
You will defeat these bosses in the final missions of these areas and they should normally become available when you are able to ride Yellow Chocobos (They are also required for 100% Map completion of Archylte Steppe). You will need to use weather manipulation machine in the Chief’s hut in order to spawn these opponents.