Skills for Nino for arena scoring.

You probably have desperation in B-slot, which can be replaced by the more expensive chill skills or dull ranged (just check the B skill list here for those that cost 240sp). Similar goes for C-slot, if you have a simple hone, spur or threaten there, you can replace it with virtually anything else. Then at last you have dual rally skills in the support slot for more score. (Also, don't forget about refinable weapons).
The changes in score would be very marginal tho and probably won't mean a consistent tier 20.

Skills with high SP costs: Aether, Double Rally, Swift Sparrow, Renewal, Chills, Ploys, Drives, Tactics would work with Nino.
However since she's an old-BST tome user she doesn't score as well as new units/melees. If you don't have already, I would advise to use the double rally.

If you want to increase your arena score, the easy way to do it is to replace Nino with someone else

B- and C-slots can be anything with 240 SP range. This build is meant to pair with Infantry Rush; otherwise you can choose another high scoring seal like Heavy Blade 3.

As others have said, it would just be better to use someone else (aka an armor emblem team) if your goal is to stay in Tier 20. I've heard some dragon emblems are no longer good enough to stay in Tier 20 recently, so keep that in mind.

You NEED dual rally and close counter. Weapon MUST be refinable for max SP points.