Blue Fire

The rose is found in the Abandonned Path, near the tall building you need to climb to reach Lady Beira. There are actually two roses : one on a little island surrounded by tombstones (The lower level, near the broken elevator). The second is found on top of one of the pillars surrounding the tall building (It's hidden by tree branches).

Bring the rose to Barri in Rust Town. Leave the place and come back, talk to him again and unlock the achievement !

I found two Roses while exploring the Abandoned Path. I think one was on top of one of the pillars next to the large tower, but I could be wrong about that exact location.

Later when you are in Rust Village look for the warrior-looking guy in one of the houses and give him one of the Roses. He tells you to come back later. Simply leave the area and come back in, when you talk to him he'll be with his lover and the achievement will unlock.