First off, you may not know this, but due to the difficulty and uniqueness of the Granbaria NG+ battle, there has also been an edited "evaluation" for it as all where Illias instead gives you help regarding beating Granbaria in the NG+ So I suggest you view the evaluation before you continue reading the rest of this post.
Now for my personal advice(some/most of it taken from the evaluation I admit), don't let granbaria lose health to the point her she gets excited while your elements are on their first summon(except fire/salamander). Because when you fight against her, reaching the point where she starts using only her most powerful techniques usually happens while the elements/spirits reach their expiration date. And believe me, surviving against granbaria's chaos stars and skull crushers is impossible while in the middle of re-summoning your spirits and healing your wounds.
That's why before granbaria reaches the point where she's going all out with her best attacks, when her health comes close to that point(but doesn't reach it yet), keep defending/healing or whatever you can do to prolong the fight, until wind/sylph, earth/gnome and serene/undine are expired, Re-summon them while granbaria is still using mixture of all her lower-level attacks, and then you can damage granbaria to when she starts going all out, the elements/spirits shouldn't expire again by the time you finish off granbaria.
Another advise is to take as much advantage of fire/salamander as possible, not only because of the useful attack boost it/she gives, but also obviously becouse of the sp regeneration, which you'll find extra helpful and even neccesary against granbaria in her later stage.
Another thing, when granbaria clones, don't use any tech, the clones were merely made as some sort of extension to her health and they disappear when you attack(each with one attack, so normal attack twice), doesn't matter what attack you use even if it was vaporizing rebel sword, so you might as well win 2 sp from making the 2 clones disappear with normal attacks instead of wasting your sp on nothing.
Oh yeah, and if you can, try to save a lot in mid-battle when you get lucky advantages/full dodges or stuff like that(yes I know, you should only save at "save locations" but that doesn't mean you can't save anywhere, it's just not guaranteed, anyway I was able to save/load a lot while fighting granbaria NG+, you shouldn't have any problem doing the same.
On top of all that, if you viewed the evaluation, illias will offer you the ability to skip that battle due to it's difficulty and maybe how it's kinda luck based too.
