Here is the full list of all 16 Destroyer: The U-Boat Hunter achievements.
No merchant losses!
First battle completed!
First sonar contact!
First U-Boat sunk!
First artillery hit!
First U-Boat hit with depth charges!
First U-Boat critical hit!
First U-Boat sunk by escort!
First U-Boat sunk by air support!
First mission completed!
Career completed!
10 U-Boats sunk!
50 U-Boats sunk!
100 U-Boats sunk!
High rank achieved!
Career in Iron Man mode completed!