To unlock 'Oliver Hazard Perry', you must sink 10 enemy ships with the USS Chesapeake.
The USS Chesapeake is unlocked during the first mission, and is available thereafter.
Some people seem to be confused about what counts for this, but simply put, all kills count.
* Kills made by the USS Chesapeake while under a ship control wild card.
* Kills made by the USS Chesapeake following your attack orders.
* Kills made by the USS Chesapeake in self defence (You didn't issue the order).
Basically, any kill counts.
The achievement is cumulative, so if you die, any kills you made before that death carry over after you reload.