As soon as you get on the island, turn around and head back to your boat and the achievement will drop for you. Here's a guide for the full crime case 1 and all 6 achievements
1 - Picked it up Achievement: 1:42
2 - Tried to Leave Achievement: 3:22
3 - Hustled Hard Achievement: 19:33
4 - Got Spooked Achievement: 21:15
5 - Picked a Winner Achievement: 30:00
6 - Answered the Call Achievement: 30:57