Both sentences are correct. These are the collocations for "goal": achieve, attain, reach

Technically, there is no difference, since aim in this context means goal, but the first sentence sounds odd and you probably won't hear anyone say it.

Hi. In this context "goal" would be the word that you would use. A "goal" is something we want to achieve. An "aim" ( when used as a noun) is the purpose or intention. I think I will have achieved this goal by next month. or My aim is to achieve this goal by next month. Hope that helps.