Well, in Tools of Destruction, the villain was a Cragmite called Tachyon. The cragmites had a war with the Lombaxes in the past and the Lombaxes banished them to some other dimension with the Dimensionater. One egg survived though, and the Lombaxes raised it among themselves, but of course it bit them in ass eventually, and Tachyon wanted to kill them all. So they all left using the Dimensionator (leaving Ratchet behind for some reason, that's still unexplained), thinking Tachyon would just give up and be peaceful. But he goes looking for Ratchet and also wants to bring the Cragmites back.
Meanwhile Clank starts seeing these weird things called Zoni that call him "Master" can give him odd time powers. Nothing's explained about them though, that all happens in this game. You find the Dimensionator during the game, but Tachyon gets his hands on it, of course, and brings the Cragmites back. Just before the big boss battle at the end, Tachyon opens a portal to where the Lombaxes are, and offers Ratchet a chance to rejoin them. But that would mean letting the bad guy rule the galaxy and leaving Clank behind, so he declines.
So you defeat him and destroy the Dimensionator. Then during the ending scene, the Zoni show up and whisk Clank away, THE END.
Quest for Booty is just filler that didn't really add anything. Ratchet finds out that a thing called an Obsidian Eye might be able to contact the Zoni. He finds one and it points him to where Crack in Time starts.