"I am extremely tired."
Translation:제가 굉장히 피곤해요.
Both work, but they are different.
"제가 굉장히 피곤해요." can be an answer to the question "Who is tired?" i.e. the subject could have been anyone.
"저는 굉장히 피곤해요." can be an answer to the question "How are you?" i.e. the listener could expect the subject would be 저, thus it is followed by the topic particle.