--First nonspell: Um... get out of the way of the bullet rays?
--Atomic Fire "Nuclear Fusion": The GIANT FACE-MELTING SUNS are aimed at you. If you can, try not to be directly under Utsuho when they're fired. If you die to this card, it will likely be via clipdeath to the blue bullets (or if your computer's like mine, from input lag). Negotiate the safest path you can find through the blue bullets and you should be fine; the card will just take a while. Alternatively, plant two or three bombs on Utsuho.
--Second nonspell: Again, get out of the way of the bullet rays. This isn't necessarily easy, especially after the red bullet spam that makes the first new wave of bullet rays very difficult to see. It's mostly a matter of seeing where the rays are aiming and getting out of the way accordingly without running into the bullets outside your immediate focus. Alternatively, learn to trivialize it.
--Explosion Sign "Mega Flare": Don't go to the sides if you can help it. Don't dodge at the bottom of the screen, or you improve your chances of getting messed over by the blue bullets. Keep an eye out for the blue bullets. Be ready to bomb if you get trapped.
--Third nonspell: Stay about a third of the way up from the bottom of the screen directly under Utsuho and watch the attack unfold. Once you have a general idea of where you can stay safely, just follow Utsuho and stay at the same distance.
--Blazing Star "Fixed Star": I don't like abusing the safe line simply because I don't trust myself to not mess up. However, knowing that it's there and where it is helps a lot for doing it the "intended way". There's really not much to say about tactics - just do ovals between the safe spot under Utsuho and somewhere to the bottom left, carefully of course.
--Fourth nonspell: See second nonspell; the WHITER THAN WHITE bullets are less dense but the giant yellow bullets make the next wave even harder to see.
--"Heaven and Hell Meltdown": There are a couple of strategies people would suggest like no-horiz, no-vert, squares, etc. but I would just recommend you play the way you feel safest as long as you don't move more than you have to (read: don't get nervous). It's up to you whether you feel more comfortable dodging in the center versus the sides of the screen, or somewhere in between - the difference is in the angles of the bullets you'll be dodging. Don't worry about staying under Utsuho; she'll come to you.
--"Subterranean Sun": Don't move too far left or right unless you have to to get through those walls of tiny clipdeath bullets. Let the gravity effect do the work for you. The bullets maintain their density for about half a second after the vacuum picks up, so plan ahead where you can.
Utsuho's hardest spells are seriously the first two. The others will mostly scare you into messing up.