Irregardless is not a word and here is why I believe it pops up in spite of this fact. Irrespective is a word that means without respect to or notwithstanding. Here is an example.
Irrespective of the fact that unthaw is not a word, it is commonly used.
Regardless essentially means the same thing, so you can replace irrespective in a sentence with regardless. Here is an example.
Regardless of the fact that unthaw is not a word, it is commonly used.
It would seem to me that people are simply mashing together, irrespective and regardless to create a new non word.
In summation, regardless is the word you are looking for, irrespective of what you might have heard.