the Big Tiger is considered as "boss" on the official website, but it is catchable, though it does not sell for a high price. The Giant Corpse Flower can also be captured too, or at least I have seen a giant cirrus-looking pet wakling around...

if you want to catch a lot of monsters only avalible in quests, this is the trick: have a quester and a catcher, during the fight, quester log off/escape, and the catcher can catch the monster. After the fight, catcher can join team with quester again, and start the battle again!!!