Моя проблема, что я нашёл предложение: Он добился успеха. So I concluded that there is no difference between this expressions and Он достигнул успеха.
You can also say “Он достиг успеха.” Грамота.ру (http://www.gramota.ru/spravka/trudnosti/36_183) states that these sentences are equally correct but my internal voice whispers me that the latter sounds a little bit better.