You learn Spells by buying them from magic shops.

The trick isn't an elixer it is a pheonix down... and I am not sure if it works on her.

I usually beat her with a Monk, White Mage, Blue Mage, Black Mage party.

If you are stuck you can always make everyone into monks and knights... both have good attack and hp... I personally prefer monks cause they are cheap and easy to equip.

Since you have no spells you will likely have to do the Monk and knight route. Perhaps a theif for his/her speed so you can quickly throw items to heal your team.

Anyways just keep an eye out for the magic shops, that is where you will get the bulk of your spells(unless you are a bluemage... they learn enemy spells) and many summons are also found not bought.

Anyways have fun this is a great game!