Explanation:

Statement I He is such an accomplished striker that he does not need anybody to give him pass from the midfield as he can create goals for himself.

Here, accomplished has been used in the connotation that he is a complete striker and can create goals for himself without any assistance.

Statement II It is an accomplished fact that the Sun always rises in the east and sets in the west.

Here, accomplished does not make any sense and established would have been correct in this context.

Statement III The whole job was accomplished well within time and that is why the students got appreciation from the Principal as well.

Here, accomplished means completed and it is correctly used.
 
Clearly, Option D is the correct choice.