Here is the full list of all 21 Challenging Dogfights achievements.
Complete mission 7.
Complete mission 6.
Complete mission 5.
Complete mission 3.
Complete mission 4.
Complete mission 2.
Complete mission 1.
Earn 3 stars at mission 1.
Earn 3 stars at mission 2.
Earn 3 stars at mission 3.
Earn 3 stars at mission 4.
Earn 3 stars at mission 5.
Earn 3 stars at mission 6.
Earn 3 stars at mission 7.
Play 30 times with the MP 51.
Play 30 times with the Cobra.
Play 30 times with the V 11.
Destroy 100 units of MS 109.
Destroy 80 units of MS 109.
Destroy 60 units of MS 109.
Destroy 40 units of Ju 87.