What about "stress-hardy personality" ? Personalidade imune ao estresse?

  Almost there, Fran, but not quite.

  I don´t think would be a good idea to express it as 'imunidade',  since it (to my thinking) means a certain insensitivity of the subject.

  Let´s say, there are very few individuals with immunity to something, what happens is that people have different thresholds of perceptions/feelings and responses.

   It´s said that everyone catch bugs (germes) through the air, for example, but only when his immunity lows he/she gets (known or unknown) diseases.

   So, 'immunity' in itself is not a meaningful word, even in science it needs a complement

'low immunity', for instance.        High immunity would be 'resistence', so 'extress resistent' or other likely choice of words; are more proper (again to my thinking).

    Plus, one has to be crack under pressure, if this doesn´t happens he will be always in dangerous territory.    

    That´s more, Sometimes a guy/gal is a daredevil stunt, but he/she is afraid of cockroach, snakes, worms etc...

    Actually, the 'hardiness' we were talking about is the qualitatively remarkable capacity some people have to endure stress, what can be seen as insensitivity in appearance, but it is not.

    PP.

"I don't think one is ever "imune" to stress but since it is for a technical translation I want to keep the translation really trustworthy to the original."

Yeah, I agree with you in this, if it is a 'street smart' translation, that´s okay using 'imune'; but if you are thinking academically you are better not.  For the very reasons above explained.

   PP.