Regret is literally translated to "arrepentimiento", so, "live without regret" should be "vivier sin arrepentimiento" but it's more common to say it like "no arrepentirse de nada de lo que se ha hecho" (ie: No me arrepiento de nada de lo que he hecho/ No me arrepiento de nada de lo que hice en mi vida)
"Viva sin pena" means "Live without sorrow" and it's an order.
"Viva sin remordimiento" means "Live without remorse" and is also an order.
And " Viva sin mirar atrás" means "Live without looking back" and also an order.
So you choose which fits best to what you want to say:)
All the best!:)