  We prove ballistic behaviour as well as an annealed functional central limit
theorem for random walks in mixing random environments (RWRE). The ballistic
hypothesis will be an effective polynomial condition as the one introduced by
Berger, Drewitz, and Ram\'{\i}rez (\emph{Comm. Pure Appl. Math,} {\bf 67},
(2014) 1947--1973). The novel idea therein was the construction of several
simultaneous renormalization steps, providing more flexibility for seed
estimates. For our proof, we indeed follow a similar path, and introduce a new
mixing effective criterion which will be implied by the polynomial condition.
This allows us to prove, in a mixing framework, the RWRE conjecture concerning
the equivalence between each condition $(T^\gamma)|\ell$, for $\gamma\in (0,1)$
and $\ell \in \mathbb S^{d-1}$. This work complements the previous work of
Guerra (\emph{Ann. Probab.} {\bf 47} (2019) 3003--3054) and completes the
answer about the meaning of condition $(T')|\ell$ in a mixing setting, an open
question posed by Comets and Zeitouni (\emph{Ann. Probab.} {\bf 32} (2004)
880--914).
