The first thing you should probably do is find out which items you're missing. You can check what you have from the Extra Contents against
LCN's item list (ignore the fact that our list has two Loreleis and a billion Einherjars; that's just because there are technically multiple versions of them, code-wise). A lot of items can be gotten from enemies, and if you click on the items you're missing it should tell you which enemy and what rank it will drop from. You can also click on the enemy name to see what specific battles they show up in which is helpful since some can be found in Practice battles. If an item doesn't list any enemies, then they can only be gotten through events. To find those items, I'd search
teruterubouzu's guide to see what you've got to do to get them.
It's a lot easier to get everything if you're playing the PSP version, since the quick save can be done anywhere instead of just between areas and does not actually get deleted when you load it. So you could save before some tough part, load that "temporary" save, and if you mess up you can just reset the game and load the "temporary" save again. You can do that infinitely until you suceed.
I'm not sure of any good ways to beat Riviera super fast. There might be an actual speed run out there, but I'm afraid I don't know where to find it. You probably want to focus on just Ein and two specific girls in each playthrough, and not bother getting skills/skill ups for the others, and even then you shouldn't spend TOO much time in Practice battles. It's possible to beat the game without ever using Practice battles, actually. Either way, definitely include the girl whose ending you're aiming to get in your party, though. The guide I linked before will also tell you what dialogue choices will please/anger which girls.
And a word of advice to you after I made the mistake of doing it myself... never chose to use a party of Ein/Serene/Cierra. They're the slowest characters and it really does make things take more time to use that party. Lina and Fia are very fast, so it's a good idea to have one (or both, especially if you decide to go the no-Practice route ever) of them in any party. Hope some of this helps!