Hard Times Are Over

Finish the game on the Hard difficulty level.
Go to chapter select and replay the game on the Hard difficulty level. Things won't be considerably different on this playthrough, with the main difference being that enemies hit for a lot of damage - some regular enemies can take you out with two direct hits. The good things about this difficulty are that all of your items from your normal playthrough carry over, and all of the chests will be restocked with new goodies to be found.

Be patient in this playthrough until you're used to how much damage you take, and never be afraid to snipe enemies from afar (or even from close range) - in many situations you can thin out a group of enemies or even clear an entire room by finding a safe perch and unleashing machine gun fire on enemies (with extra help from some time rewind clones).

Abuse Earthquake on Hard difficulty: it requires no magic gauge and can be used endlessly; any time you're being mobbed pull this move out of the bag to clear some space and get clear.

Shadow Friend and Rage Saving are the big life savers for this playthrough - if, for some bizarre reason, you chose not to acquire these abilities from the altar in your first playthrough, do so immediately: Shadow Friend will be indispensable against a few bosses and even during some regular encounters; Rage Saving allows you to cast more than one spell consecutively as long as you have enough magic in your gauge.

A final tip is to micromanage your equipment; every item has at least one buff attached to it, and if you're having a hard time with anything you can swap out equipment to suit your current predicament. An example of this would be if your health gets low enough that Shadow Friend is activated: Shadow Ayumi can wreak a great deal of havoc, and as soon as she's activated you can press Select Button to go into your equipment tab and equip the Figured Amulet and the Magic Ring, both of which buff the effectiveness of Shadow Friend - now watch Shadow Ayumi singlehandedly slaughter 3 or 4 enemies all on her own. You can swap out equipment as often as you like, and the buffs take immediate effect, so play around and see what works for you.