In order to unlock this achievement you need to make your way to the British Racing Green Horizon Story and select the first chapter: "Second Century". You only need to complete this chapter in order to unlock this achievement and as such do not require to get anything more than 1 star.
In order to meet this criteria, you need to first complete the preamble. Then the challenge is divided into two further parts:
1- Reach the destination within 5 minutes whilst staying above 113 km/h (70mph), driving the DB5
2 - Drive the DB 2016 to the destination within 5 minutes (3 stars would be 2 mins 30s).