Yeah, Fire Artist's reply only applies to non-residents -- or if Ireland considers you to still be resident (per the tax treaty) while you are living in Canada.
I think a 2 year work visa would normally put you (eventually) as "resident" or even "deemed resident"? (e.g., if you are on vacation here for more than 183 days and do not keep residential ties in Ireland).
Do you intend to move to Canada and make your primary residence here? Will you remain for more than 183 days each year? - Resident / immigrant, and you declare your move / entry date on your first tax return.
If you reside primarily in Canada for more than 183 days a year, with the intent to stay, you pay Canada taxes for the portion of year after you arrived.
If so, this is how it works for resident aliens:
1. You pay taxes on world income earned while you were deemed resident in Canada, via your tax return. (date after you entered canada).
2. On the CDN tax return you state how much $ taxes were paid to foreign countries for the income earned while you were deemed resident in Canada. This is subtracted from the taxes owed to Canada.
Basically, it's a wash, you don't pay double taxes, but will pay the Cdn tax rate, which might be higher than Ireland.
For some work visas, you may be considered to remain a resident of Ireland despite living in Canada (e.g., Irish military stationed here while you maintain a home in ireland? work for the embassy? Some oil and gas companies with camps, etc). some very temporary visas... You need to figure out if Ireland would still consider you resident even after you move here for the visa.
A deemed resident would need to be considered a resident of their home country still, even if they reside in Canada for more than 183 days. Would Ireland think that you are still resident there? We have a tax treaty, so the "deemed non-resident" rules would apply, and Fire Artist is correct -- Cdn taxes on Cdn sourced income only.
I just can't imagine what type 2 year work visa, especially after you make an application for permanent residency (while on work visa), would keep you as a resident of Ireland while living primarily in Canada.