When doing a field theory that comes out with a tachyonic solution (such as bosonic string theory, which is not a valid theory in itself), the tachyon has negative rest mass squared. The rest mass is imaginary (the rest mass is an imaginary number like the
sqrt(-1)*m,
where m is a real number,
since rest mass = sqrt(m²).

That is why we consider these to be bad theories and they're unstable (i.e. even if such a solution existed the universe wouldn't stay in that state, like a ball sitting at the top of a very narrow hill: given even the tiniest push or gust of wind it would roll down to a state where there were no tachyons). But in those non-valid theories, the speed of a tachyon would depend on how much energy you gave it. It is much like our own massive particles here; the mass and speed depend on how much energy that has.