Evolving weapons happen by combining a max level weapon with any level of a specific secondary support item. Once you have both of those items you must then kill an Elite enemy and open the chest that it drops. The combinations for the Gatta Amari is the following:
Vicious Hunger – Gatti Amari + Stone Mask
The Stone Mask is first found in inlaid library, once you find it you can unlock it as a level up item for other levels (It is also found as a stage item in Inlaid Library and Moongolow.)
Gatti Amari is the starting weapon for Giovanna and can be unlocked for other characters after surviving for 15 minutes as Giovanna (Giovanna is the unlockable character in the coffin within inlaid library).
If you're interested in seeing what the combo is for the other weapons they are listed below in the spoiler tag :)
*** Spoiler - click to reveal ***
NO FUTURE – Runetracer + Armor
Unholy Vespers – King Bible + Spellbinder
Bloody Tear – Whip + Hollow Heart
Hellfire – Fire Wand + Spinach
Death Spiral – Axe + Candelabrador
Holy Wand – Magic Wand + Empty Tomb
Thousand Edge – Knife + Bracer
Heaven Sword – Cross + Clover
Unholy Vespers – King BIble + Spellbinder
Soul Eater – Garlic + Pummarola
La Borra – Santa Water+ Attractorb
Thunder Loop – Lightning Ring + Duplicator
Gorgeous Moon – Pentagram + Crown
Mannajja – Song of Mana + Skull O'Maniac
Valkyrie Turner – Shadow Pinion + Wings