How do I perfectly match the paint on my wall?

I moved into a new apartment. The walls are painted this light green color. I like it but there are a lot of places that have some paint peeling off and spots that needs Spackle – etc.

The walls were painted this color like ten years ago and my landlord doesn’t have the paint or can even tell me what was used. I know Lowes will color match but what do they usually require? Should I peel off a little paint flake and bring it in? Is color matching perfectly even possible?

How can I paint over the peeling spots on my wall without having to do the whole wall? Any ideas?