I not only want to improve my English ability, I want to become more mature.
My goal is to not only improve my English ability, but to become a more mature person overall.
「英語だけ実力をあげるのではなく、自分自身も一皮剥けたい」= I not only want to improve my English ability, I want to become more mature. / My goal is to not only improve my English ability, but to become a more mature person overall.
ボキャブラリー
not only = だけではなく
improve = あげる、上達させる
English ability = 英語能力
become more mature, become a more mature person overall = 自分自身も一皮剥ける
goal = 目標