Does anyone have a translation for:

''Everything happens for a reason''
''No regrets''
''Life without regrets''

I'm looking for a quote or saying in Irish to get as a tattoo, something along those lines but I'm open to other ideas too

For - No Regrets - I suggest - Níl aon aiféala orm.(but wait for the others to give their opinion)
- and for - A Life without Regrets - perhaps : Saol gan aiféala, (if that isn't too literal).

Tharlaíonn gach rud ar chúis éigin
Everything happens for a reason

Gan aiféala
Without regrets
Aiféala ar bith
No regrets

and, as franc suggested:

Saol gan aiféala
Life without regrets

or, somewhat more completely:

Caith do shaol gan aiféala
Live your life without regrets

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I'm not a native (or entirely fluent) speaker, so be sure to wait for confirmations/corrections, especially for tattoos.

A couple of suggestions

Tá fáth le gach rud a tharlaíonn
There is a reason for everything that happens.

Tá fáth ag gach rud.
Everything has a reason

There may well be better ways of saying it

I would use "le" instead of "ar".

Sounds good.