Definitely a Caulerpa species - the question's really just which one.
The tips of the "leaves" being rounded eliminates quite a few (C. taxifolia, C. mexicana, C. sertulariodes, C. scalpelliformis, etc.) - it leaves us with options like C. articulatus, C. ashmeadii, C. cactoides, etc.
The "stalk" of the algae looks pretty smooth for C. articulatus and C. cactoides, but maybe you can see if it has those "notches" in it that are typical of the species; the "leaves" look slightly too short and stubby for C. ashmeadii.
Anyway, with several dozen species in the genus, I would expect it to a Caulerpa species closely genetically related to C. articulatus, C. ashmeadii, C. cactoides, etc., but I'm not sure exactly which species it would be (I would guess it would fall into the "etc." category though).