This monster is my transportation?
You can't ride Mamadoodle. Guess she's one of the monsters that's not the right shape to be ridden. If you want to know about specific individual monsters, just Google 'em. There's ample info about every RF4 topic imaginable across the internet.
EDIT: Thought I should mention, in case you didn't know...boss monsters can be tamed. As far as I know, they cannot be tamed the first time you face them...you have to have defeated them once. But if you go back and fight them again, it is possible to tame them. But they have specific items they want, and even then, they're still difficult, so it's best to save before trying, to get back the rare/difficult items you used if your taming attempts fail. (It's easier to tame monsters who are a lower level than you, though it's possible to tame a monster of any level. It's just likely to take a lot more tries.)
EDIT: Thought I should mention, in case you didn't know...boss monsters can be tamed. As far as I know, they cannot be tamed the first time you face them...you have to have defeated them once. But if you go back and fight them again, it is possible to tame them. But they have specific items they want, and even then, they're still difficult, so it's best to save before trying, to get back the rare/difficult items you used if your taming attempts fail. (It's easier to tame monsters who are a lower level than you, though it's possible to tame a monster of any level. It's just likely to take a lot more tries.)