The story
Probably a blend of irrespective + regardless. The word may also be analysed as ir- + regardless, as it is possible that the prefix ir- was added to amplify the negative in regardless just as plain negatives often did at the time the word came into use (and still do in dialects).
First known use, by meaning
- from mid 19th century Irrespective, regardless.
Etymology from Wiktionary, CC BY-SA 4.0.