BTW doing all the worlds in critical will unlock the proud trophy at the same time.
Not really sure if I can offer any tips, other than what you should already know from playing previous KH titles. I can very much recommend getting the ring that gives you the round block ability as early as you can, and the block charger ability as well. Make use of cure spells, spells like magnega, also the finishing plus abilities (2 of them) are very useful. I did my playthroughs in Critical both times (Jap and Eng), so I'm not really capable of offering advice on the differing levels of difficulty, but as long as you use your level chips smartly you should never really have a problem.
Sorta spoilers for a particular bit that caused me a bit of trouble In the second 3D shooter segment, at the end of the 7th world, Hollow Bastion 2, there is a Darkside who caused me quite a bit of trouble as he is very hard to lock on to and shoot without leaving yourself very open to attack. I very highly recommend getting the blizzard ability in that section and saving it until you encounter the darkside, then spamming that ability until he's dead, pausing only to block, as it will home in on him and do decent damage, plus it has heaps of 'shots' before it runs out.
I somehow made it to the coliseum on critical mode at level 8. :/ I drank a redbull it helped. I also just did my best not to get hit, only took two hits to kill me, but as long as you dodge and heal every second, you should be fine.