Chain Gauge:
We all know that RAV attacks cause the chain gauge to decrease more rapidly than COM attacks, but the actual attacks you use make a difference too. If you use 4 different attacks (Fire/Thunder/Aero/Blizzard) the chain gauge will decrease much slower than if you did (Fire/Flamestrike/Fire/Flamestrike). And if you do (Fire/Fire/Fire/Fire) it will speed down to 0 almost instantaniously.
The computer takes care of this 90% of the time, it was just frustrating for me seeing it constantly using sub optimal attacks.

Upgrading Items:
Always get items up to a 3x EXP multiplier before you add components to them. It takes ~32 of the exp multiplier raising items to get to 3x. At that point do a big dump of your highest exp items.

Do all item leveling in one go! If you have an item and you use 20 100exp items it will gain 2000 exp and go up a bunch of levels. If you use 10 items one time it will go up a few levels, and items won't give as much exp per item so the last 10 you add will only give you something like 80exp per. Like most customization systems it kind of screws you over unless you know it inside out and have a plan from the moment you pick up the game.

Power Shifting
If you recover two full ATB bars since the last time you have shifted paradigms the next shift will cause you and your party to have a full ATB bar after the shift. In other words, if you time your shifts properly you get 3 actions for every 2 charges of the ATB bar.

Illustrated:
Recover Full ATB -> Use Full ATB -> Recover Full ATB ->Use Full ATB -> Paridigm Shift -> Use Full ATB -> Recover Full ATB -> Use Full ATB -> Recover Full ATB ->Use Full ATB -> Paridigm Shift -> Use Full ATB

IMO this is the only character interaction part of the game, timing my shifts so it benefited my party the most while trying to keep on top of the power shifting to get free turns was the interesting part of the combat system. It isn't even explained in game, so if you never found out about it I could understand how people would find the combat completely uninvolved and boring.

Enjoy.