You would certainly have to resolve the ambiguity between yo and ella, because the conjugation is the same. But you can omit the pronoun for tú:
Mientras ella estaba feliz, estabas cansado y yo estaba triste.
But it would sound weird, unless the previous sentences were speaking about tú.
It sounds better with the pronoun for tú, because later you specify yo.
Besides, if the sentence comes after one or more that speak about ella, you could omit the ella in this one:
Mientras (ella) estaba feliz, tú estabas cansado y yo estaba triste.
But, since it is an opposition between ella, tú y yo, it sounds best with all the pronouns.
That said, what I would omit is the verb for yo, because it is the same as for tú:
Mientras ella estaba feliz, tú estabas cansado y yo triste.
Note that if you use usted instead of tú, the three verbs are the same and you can't omit the pronouns, without making the sentence impossible to understand:
Mientras ella estaba feliz, usted estaba cansado y yo estaba triste.