Can a nurse with working visa can go to canada withoutletter of eligibility?

You should ask those questions in the international forum.

Your work permit is only good for one employer only and limited (normally for 1 year), and I guess you haven't recieved the work permit yet, just the letter from the embassy, since you normally get the work permit at the border.
And so, no you cannot just go to Canada and work sth, only that job what is outlined in your workpermit and only for that employer. So you will need the eligibilty letter to be able to register as a grad nurse, without registration you cannot work.

5cats

Gelie Grace, base from POEA (PI forum)

You can not be deployed or leave the Philippines if you dont have your VISA and ELIGIBILITY.
Like in your case you were give a TWP without eligibility which is very likely to happen.
You should contact your employer and ask if they were notified about the result of your Nova Scotia assessment.

I think you should comply with the requirement as given to you by the CRNNS. Base from your previous post you lack hours on theory. Furnish them with the necessary documents like a post graduate transcript etc
after complying with this, resubmit your application. Then be give an eligibility. This is a long shot but that how the cookie crumbles in this case.

Or go back to your nursing school double check your theory hours. Maybe there was a mistake on your transcript. Then get reassess.

Work permit is issued at the border when you arrive in Canada. It is only for the one employer so you can't work for anyone else and even stipulates on the work permit employers name and conditions. Can be from 1 to 3 years and that is decided at the desk when you arrive. Some really good advice here and you need to check with your employer