How can I make my email better?

I wouldn’t start and not mention it at all to say that you “hope she remembers” as that could suggest that you think she might be at fault or that she has a sieve for a brain.
“I’ve been waiting expectingly for a result on my job interview that we had six weeks ago.”, is something you could write.
By the way, I don’t know who much time has passed after the six weeks, but if it is only some days I would suggest to give them a few more days to send them a message.
When mailing about job applications I think it is adviced to be as formal as possible.
No “Hi’s” and “Bye’s”

I’d be more formal and less impatient:

Ms. HR Lady

I’m looking forward to details on my acceptance by your firm. If you could let me know the anticipated start date, it would be much appreciated; being ready to begin at—- has been my focus for the last six weeks.

Thank you for any information you can send at this time,

Sincerely,

Micky (whatever your last name is)

Use the most polite form of her name and yours.

I assume the person you will be communicating with is not the decision maker, right? So the upraised pinkie letter (see @zenvelo)‘s isn’t useful or welcome. You’re working with someone for whom this is a clerical task. You should keep that in mind.

There are three cases:

1. You’ve been kicked off the island. In that case, a simple, “Could you tell me the status of my application?” should get the info.

2. They are still processing. In that case, you don’t want to be annoying. Sometimes people are annoyed by check-ins, sometimes they think it shows initiative. In any case, don’t take up a lot of their time. So “Could you tell me the status of my application?” should still work.

3. They have FORGOTTEN about you. In that case, “Could you tell me the status of my application?” should get them back on track.

“I hope you remember I got selected in the company. I have been waiting for updates and I haven’t got any. Please can you tell me the status?”

I have been selected by the company for hiring. The six-wwk waiting period is now over, and I have not yet been notified.

Please let me know the status of my employment.

Thank you.

Sincerely,

Hi, Ms. (whatever her last name is),

I just wanted to follow up with you and check on the status of my paperwork. Can you confirm my start date? Thanks!

(Your first and last name)

Thanks a lot guys! I am going to send it by EOD(End of the day). Once again, Thanks!