Usage panels—and other smart people—consider the use of irregardless as a huge blunder. It simply isn’t a word. Someone couldn’t figure out how to use irrespective or regardless and married the two, and irregardless was born.
Stamp it out.
Some usage panels do say it is a word but counsel against its use. Here's Merriam-Webster:
Irregardless originated in dialectal American speech in the early 20th century. Its fairly widespread use in speech called it to the attention of usage commentators as early as 1927. The most frequently repeated remark about it is that “there is no such word.” There is such a word, however. It is still used primarily in speech, although it can be found from time to time in edited prose. Its reputation has not risen over the years, and it is still a long way from general acceptance. Use regardless instead.