。
Don't believe him no matter what he says.
Literal
Even-if-たとえ he [subject-が] what [object-を] say-ever-volitional-と even, don't-trust.
~ようとも is the volitional + も pattern — 'no matter what one does, even X-ing.' A concessive meaning 'regardless of whether X.' 何を言おうとも = 'no matter what (he) says.' 信用するな is the negative imperative.