The equation to measure relativistic time dilation is
t = T * (1 - v2/c2)(1/2), where t is time on board the spaceship or whatever, T is the time measured by the observer, v is the velocity, and c is the speed of light. Notice what happens if v is greater than c: the expression inside of the parentheses becomes negative, so when you take the square root of that (1/2 power), the entire expression becomes an imaginary number.
I don't think anybody can really evaluate what the universe would look like with imaginary as well as real dimensions. The same equations that indicate that your tachyon would experience imaginary, rather than real, time, would also cause it to experience imaginary space as well. These are so far out of our ability to observe them that it's very difficult to test any speculations we might have.