You Do Need power plug adapter while traveling from Costa Rica to Saint Barthélemy.

Here is Why You Need An Adapter

The outlet and plug type used in Saint Barthélemy are C and E and in Costa Rica are A and B. This is how they look like.

Costa Rica

In Costa Rica, outlets of type A and B are in use.

Type A

Type B

Saint Barthélemy

In Saint Barthélemy, outlets of type C and E are in use.

Type C

Type E