Where to farm rank 3 Monster Materials?

I thought Chocolina sold them but she doesn't. Maybe because I didn't finish the game?

I need the materials for my Chichu but I can't find them!

Solution 1:

Chocolina stops selling the potent monster materials after the first grade. She does, however, start selling Power Orbs, Mana Orbs, Vitality Orbs when you get to Academia -500 AF-, but that's towards the end of the game.

Here's where you can farm the materials:

Potent orbs

Buccaboos in the Stonestump Wastelands and Grave Ridge areas of the Archlyte Steppe -??? AF- when it's sunny
Ghouls in Academia -400 AF-, but only before you reach New Town²
Garganzolae and Apotamkins in A Dying World -700 AF-¹
Winning the Orphan Derby, Lindzei Cup, or Pulse Cup in the Fal'Cie class Chocobo races at Serendipity -??? AF-

Potent engines

Flans in Augusta Tower -300 AF-, but not on Floor 13
Munchkins¹ in the Bresha Ruins -300 AF-

Vitality orbs

Miquiztli in Academia -500 AF-
Vodianoi and Samovira in the southern portion of the Grave Ridge region in the Archlyte Steppe -??? AF- when it's cloudy
Bunkerbeasts in Yaschas Massif -100 AF-
Green Chocobos in the -1XX AF- eras of Yaschas Massif
Winning the Atomos Derby¹ in the Fal'Cie class Chocobo races at Serendipity -??? AF-

Vitality engines

Zwerg Metrodroids¹ in Augusta Tower -200 AF-

Power orbs

Tonberries that appear in rifts in the Brescha Ruins -300 AF-
Buccaboos in the Stonestump Wastelands and Grave Ridge areas of the Archlyte Steppe -??? AF- when it's sunny
Pitterpatters in Yaschas Massif -100 AF-
Barbed Specters in the Stonestump Wastelands and Grave Ridge areas of the Archlyte Steppe -??? AF- when it's cloudy
Winning the Carbuncle Classic¹ in the Fal'Cie class Chocobo races at Serendipity -??? AF-

Power engines

Yaksha and Yakshini¹ in the Vile Peaks -010 AF-
Shaguma and Haguma¹ in the Vile Peaks -010 AF-

Mana orbs

Xolotl in Academia -500 AF-
Sahagin Princes in the Assembly Area region of the Sunleth Waterscape -300 AF- after completing the main story events
Winning the Anima Stakes¹ in the Fal'Cie class Chocobo races at Serendipity -??? AF-

Mana engines

Vespid Solders¹ in Augusta Tower -200 AF- mostly on the 51st floor

^{Note 1:} My personal farming recommendations: they tend to have far better yields or are more mindlessly farmable than the alternatives.

^{Note 2:} They'll show up again if you close the gate.

Solution 2:

Just about everything A Dying World -700 AF- Drops potent orbs. The only monsters that do not are the untameable Cie'th monsters.