Formal:
* Anuman ang mangyari - Regardless of what happens
* Kahit ano pa man - No matter what
* Walang kinalaman sa - Regardless of
Informal:
* Kahit na - Even if
* Anuman - Whatever
Example:
* "Irrespective of the weather, we will go hiking."
* Anuman ang panahon, maghahiking pa rin tayo. (formal)
* Kahit na ano ang panahon, maghahiking pa rin tayo. (informal)
Note: The context of your sentence will determine the best translation. Consider the formality of the situation and the specific nuance you want to convey.