Achievement (ぎょうせき) 

きょう、,わたしはひとりじぶんでぎんこうにいってきました！
それはわたしにとってのはじめて(のこと)しょかいででしたす。

I want to say today I went to the bank by myself and it is my first time. :3

*We sometimes have to change, add or take off the words when we translate, to make the sentence natural in each languages. For example, ぎょうせき is one of the correct translations however, it doesn't sound natural, at least to me, I would add more words in Japanese, like "an achievement (I) could do today" in literal translation. (きょうたっせいできたこと)

Good job, please keep practicing. I hope this was helpful. 

Achievement (ぎょうせき）

きょう,　わたしは　じぶん　で　ぎんこう　に　いってきました！
それ　は　わたし　の　しょかい　です。

I want to say today I went to the bank by myself and it is my first time. :3

Well done, that attempt was close. Just swap "today" from the beginning to the end of the sentence.

I went to the bank by myself for the first time today.