When you reach the open ended part of Final Fantasy XIII you can take on monster hunting missions. Daisuke Inoue, Final Fantasy XIII Battle Planner, designed these side quests with four rules.
Monster missions are the main after-the-credits-roll content in Final Fantasy XIII. Expect a challenge, if you decide to keep playing.
Source: Siliconera
1.) They should never force the player characters to equip any specific accessories.
2.) They should never require players to use TP abilities* to defeat them.
*(TP abilities are special skills such as Quake, Libra, and summons.)
*(TP abilities are special skills such as Quake, Libra, and summons.)
3.) They should never require the player to use healing items to defeat them.
4.) They should never require the player to use shrouds* to defeat them.
*(Shrouds or smokes are buffing items you can use before encounters.)
“I can assure you that the mission monsters were designed first and foremost to present players with a real challenge,” said Inoue. “So much so, in fact, that our producer Mr. Kitase even came to us complaining he could not beat some of them and had no idea what to do, despite fighting with none of the handicaps mentioned above.”4.) They should never require the player to use shrouds* to defeat them.
*(Shrouds or smokes are buffing items you can use before encounters.)
Monster missions are the main after-the-credits-roll content in Final Fantasy XIII. Expect a challenge, if you decide to keep playing.
Source: Siliconera
This should be really interesting to try out then. I'm actually looking forward to facing these tough monsters. It will probably be frustrating, but you'll certainly be feeling warm and fuzzy inside whenever you do kill a crushingly difficult quarry.
I'm guessing this'll be the most challenging FF so far. Sounds dead exciting. 
If Kitase is having trouble killing the mission monsters in XIII then I guess this will be the most challenging Final Fantasy yet. I cant wait to play and get all the acheievements and Defeat these tough monsters to earn em. OMG 7 DAYS 