We can tell you how to say this word correctly, but we bet you just keep to the same way you've been saying it for years and carry on regardless. This is a really strange one. For a start, there are people right now looking at the word "regardless" and imagining there are extra letters placed in the front of it. Another one where we have taken a pretty simple word and turned it into something more complicated.
No, this word is not "ir-rig-ard-less". Irregardless isn't even a real word, it's a contraction of "irrespective" and "regardless" that most dictionaries refuse to recognize. Because there's no double 'r' sound at the start, it isn't "rig-ard-less", either. Let that 'e' do its work, and let the word sound out the way it's supposed to - "ree-gard-less".