IF Formula with Sum inside?

Having a moment & can't work out if I'm doing something wrong or it isn't supported.

I'm trying to make an if formula based on if a target has been met, example below rather than a sheet.

A1 will hold the target & B1 will hold the value. In C1, I want the formula to generate based on the below.

Greater than A1 then "Achieving"
Less than A1 minus 10 then "Under"
Less than A1, but greater than A1 minus 10 "Improvement"

Hope that makes sense & hopefully the solution isn't staring me straight in the face.