Here is the full list of all 21 Challenging Dogfights achievements.
Earn 3 stars at mission 1.
Complete mission 7.
Complete mission 6.
Complete mission 5.
Complete mission 4.
Complete mission 3.
Complete mission 2.
Complete 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.