"Irregardless" vs. "irrespective"

Solution 1:

The "ir" in "irrespective" means "not", i.e. "not respective". So "irregardless" would mean "not regardless", which would mean the opposite of what you probably hope it would mean.

Solution 2:

Some people use "irregardless" for “regardless” but many people think it is incorrect. It is probably a combination of "irrespective" and "regardless" which is sometimes used humorously.

Oxford Dictionary says:

Irregardless means the same as regardless, but the negative prefix ir- merely duplicates the suffix -less, and is unnecessary. The word dates back to the 19th century, but is regarded as incorrect in standard English.