What to do with a neutral Minerva?

Well mine is -atk but with flier buffs and heavy blade seal and eff hauclere she can become and enemy phase monster.
With desperation and goads she will be able to proc boosted lunas/bonfires/draconic auras.

You can also go an enemy phase build. Thanks to eff hauclere she can actually run fortress def for a nice 37 def. Then proceed to either spam moonbows or set up other specials for ohkos

Minerva usually wants to run a hyper-offensive build, to compliment her stat line. Something like this:

Hauteclere (+Eff, +Atk or +Spd refine)
Reposition
Draconic Aura
Life and Death 3
Drag Back/Vantage 3/Hit and Run
Flier boost skill

My Minerva is +atk -res, but even with a neutral one, I think my build would work :

Weapon : Hauteclere (+eff)
Assist : Reposition (best assist for fliers)
Special : Moonbow
A : Life and Death 3
B : Desperation 3
C : Ward Fliers (flexible)
Seal : Brash assault 3.

With Hauteclere, moonbow is only at 1 cooldown, meaning that on the first encounter at enemy phase, it will trigger... and one shot an Effie or a Brave Ike, for example. And if you ever go below 50% HP, you will automatically double your opponent, triggering an enhanced moonbow in the process. If you feel confident in your ability to double your opponents (because of flier buffs for example), you can go for the heavy blade seal and Draconic Aura special for more destruction on the player phase (not even reds would be safe), but you lose the bait power on first encounter, which is quite an easy way to put Minerva in desperation range, or even brash assault range depending on who is baited.