I recently got Final Fantasy XIII-2, and I wanted to ask: how do you capture a behemoth? I defeated my first one after getting killed like 20 times and plus I'm new to the Final Fantasy series, so now that I know I can beat it how do I capture one, because I need it to beat Caius (first encounter).
Obtaining the Monster collector fragment skill increases your changes by 20% as stated in the other answer however there is also another way to increase your chances.
Using the Feral Link ability increases your chance of capturing a monster, the synchronisation percentage is an indicator of likely you are to capture the monster and these stack so the more times you use feral link the more chance you have of capturing the monster. The percentage of each interaction is determined by how well you preform the quick time event. This is stated, in part, in the game manual, page 40. Also Killing the monster with the feral link attack gives a bigger bonus to your chances of capturing it.
You can equip accessories to increase the speed of the feral link charge speed, I forgot the name of the accessory but I have it equipped so will check when I get home.
I have read online that getting a 'Great' strike when you initiate battles and getting a 5 star rating also increase your chances of capturing but I can't find conformation of this anywhere. I will look further tonight but I think these are not relevant to your chance of capturing a monster.
The easiest way to capture a behemoth that I know of is to have a Pulsework Knight, preferably one that’s level 20, with you. When it uses Provoke, the behemoth will only focus on him, and the behemoth can hardly take any health off the Pulsework Knight.
The behemoth can’t even take the level 20 Pulsework Knight out in one shot using Heave so you can take out the behemoth easily and get all the max number of stars for the battle.