This is a badly formed word. It has no place in academic writing. Indeed, AWE doesn't think it has a place anywhere - except that it is to be seen and heard all around. It is essentially a good word (regard) used with two negative affixes. (Two are too many, and one is not used with regard anyway.)
The word regard is used, with different meanings, in several contexts. The context in which
irregardless is most often to be found is related to the use of the participle regarding, or the prepositional equivalent 'with regard to': "with regard to the theories of Professor X, we must point out that she wrote regarding the effects on the economy of a fall in the inflation rate."
The opposite of with regard to should logically be 'with no regard to' or 'without regard to'. The meaning of this can be expressed by the word regard + the suffix less. What does not exist in idiomatic English is a word formed by the prefix ir- with words formed from the root of regard. If such a word existed, it would still be wrong to use both negatives, the prefix and the suffix. To do so would essentially be to use a double negative - and therefore an error in academic English. (See Negatives - double negatives).