They are very similar and are listed as synonyms for each other. Attain (verb) 'to reach'. He attained the age of seniority and permanent status. Achieve (verb) 'to win'. He achieved top honours and a gold medal.
The smart student study very hard to achieve his/her homework very early. The hard-working employee spend a lot of time on useful research to attain more profit to the company who is working for. To achieve your dream you have to concentrate you on it. To attain your dream you have to concentrate on it. To acquire Master's degree you need