Shining Resonance Refrain

The first Rare monster you'll come across is during the first story mission of Chapter 3. You'll have to fight an Orc, and right behind that Orc in the woods you'll see a large gryphon. Kill that to unlock the achievement. Rare monsters will show up often as large red dots on the map. Most of the time they have a unique name, and are often affected by the weather. You'll likely come across a rare monster on accident, but the gryphon is an extremely easy one to find.