There are five manuals

1:Calm Land-u can find in the chocobo dungeon

2:Mihen Highroad-Near the area before u approach the Mushroom Rock Area,u press X when u are up to one of the machina and u receive a manual

3:In Djose temple take the left door before going up the steps and talk to the man,he will give you a manual

4: Outside of the Djose Temple and to the back of the digging registration building there are some monkeys.When they all jump up in unision(at the same time) press X and u will receive a manual

5:Lastly,near the area where u fought Ixion,talk to the guy and when he asks for the password say MARNELA

There ARE five manuals. The fifth is in the Cave Ruins.
You need to defeat the Anything Eater before you can access the area it's in, but it's definitely there. It's just a really complex dungeon.

The Experiment has five levels and three different attributes (defense, attack, special). Digging for assemblies in Bikanel will strengthen the different attributes. You need to level up every single attribute to the max to get the Experiment to level 5.

The reason you collect the manuals is to repair it so you can fight it at level 5 (and you'd want to do that for the reward, and/or if you're gunning for percentage). For example, if you fight it at level 2 because you haven't collected enough attributes, you can repair it and try again when it's stronger. You don't NEED every manual, unless you choose to fight it five times.

You can avoid going out of your way to collect the Cave Ruins one by only fighting it again once it's level 5. You don't need to fight it every time it levels up and repair it again.