I would never say "y a mi vez logré" it sounds strange to me. I would say "y a la vez logré" that means: "and at the same time I managed..."

'A mi vez', 'a tu vez', 'a su vez' etc. (all persons are possible) are very rarely used in spoken language, unless in well educated environments. More often (although not that much either) you'll see them in written language. Some examples: 'Mi abuelo enseñó a mi padre a pescar, mi padre, a su vez, me enseñó a mí y yo, a mi vez, a mis hijos'. 'Ella me habló de su familia y yo, a mi vez, le hablé de la mía'. In your sentence, 'a mi vez' could be 'when it was my turn' or 'in due time' or something like that. For a more accurate translation I would need more context.

es algo que se una muy poco, es mas comun oir decir "a su vez" soy hispanohablante asi que no te preocupes

i think ..for me

In my opinion it this context " y a mi vez" would mean "and at the same time" There might me a better translation for it though...