We discuss the phase diagram and the universal scaling functions of attractive Fermi gases at finite spin-imbalance determined within a Luttinger-Ward formalism. The results indicate that beyond the Clogston-Chandrasekhar limit at $(h/\mu)_c\simeq 1.09$, the unitary gas exhibits an inhomogeneous superfluid phase with FFLO order. On the fermionic side, near unitarity the critical temperature for this transition can reach up to $\simeq 0.03 T_F$.