Nana's main Artifice is her AP Increase to the backmost group, which increases the AP cost of all their moves by one - quite debilitating.
Her secondary Artifice is her Fortitude stacking, which builds up over the course of the battle and can unpleasantly extend the battle.
If you wish to bring a full space team to the fight, bring no more than one backliner. Having more than one girl on the team with AP increase is far too debilitating. Or, as the teams below prove, let Nana stick her AP increase on a fodder who dies in a single hit.
As for her fortitude, multihit attacks such as Amaterasu Hikari's CX can prove effective, or you can simply brawl it out for a little longer.
The extensive amount of space offensive power accessible to players trivialises this boss. Place an auto-taunter on a different row from your main damagers to soak up the AP up, and then proceed to defeat her.
1) Standard Full Team
Well, yes, you could do this the way Ateam intended you to do it. You could, but I don't know why.
Save Amaterasu Hikari's CX for burning through Nana's fortitudes. Try and get off some Nutcracker buffs/CX before using the other ones.
2) Pandora/Nutcracker/Onikage/WokeTamao + Sun Maya
Once praised as the holy grail of clearing methods for EN players who have access to high Unit Skill Sun Nation General Maya, this method has fallen out of favour due to other easier and more reliable methods.
The general strategy is to have the mid and back fodder die as quickly as possible, and begin a cycle of Maya taunting every turn, and the attacker filling up the rest of the AP. Each of the three have their quirks - for Onikage, you must stack lots of evade with her 3AP. For Pandora, you have to poison the boss before using her CX. For Nutcracker, avoid using her 2AP buff - hitting the boss is better.
It is possible for the backline fodder to survive until the end of turn 2 if Nana queues her moves in a certain way, but by then the chopper has likely taken too much damage. It is precisely this gamble which makes this strategy unreliable.
3) This was once considered fast.
Using two space nukers and Snow White's poison and AP down, defeat Nana in five turns.
1) Siegfeld's Imouto
Awakened Shiori can defeat Nana on auto, with a backline fodder for the AP Up. Every single time Shiori moves, she heals herself, after all.
Both of these can have one MaxHP% burn/poison girl added to the team to speed up the run.
2) Shakespearean Tomboy Fairy
Fairy Puck Futaba, with a single backline fodder, can solo Nana. Use a defensive memoir on Puck - standouts are the 4★ Dance of the Gods which grants 5999 HP, and 4★ Equine Friends which boosts her ACT Power while giving 15% Cloud damage down.
On the first turn, queue Puck's counterheal followed by her AP down, and subsequently queue counterheal, AP down, brilliance strike, brilliance strike. Cast Puck's CX the turn before Nana's if possible, or in order to remove fortitudes from Nana.
3) Accelerator, but it's not Railgun?!
While one of the most innovative strategies, it's unfortunately very, very, slow - taking up till turn 26 or 27 to defeat Nana. However, it's entirely safe, unlike the Chopper + Maya strategy. Use Pollux's reflect every turn, followed by Perseus' barrier and heal. Queue Perseus' CX the turn before Nana's so you can have 90% reflect on Perseus when Nana casts her CX.