Nice to meet you. I am Mari. How are you?

Original:はじゃまして. わたしわまりです. おげんきですか 

Correction:　はじめまして。わたしはまりです。おげんきですか。

With Katakana and Kanji:　はじめまして。私はマラです。お元気ですか。

Introducing Myself

はじめまして. (わたしは)メアリー（めありー）です. おげんきですか

Nice to meet you. I am Mari. How are you?

(I only know hiragana if any tips, please leave down below.)

So yeah, we have that typo with はじめまして and your name should be (well, unless your name is Marie or some language that pronounces it like まり) written (and pronounced) as めありー. Other than that there aren't any mistakes that I can spot. Also, you can probably omit わたしは here as it's pretty apparent that you're speaking of yourself in a self-introduction.