In theory, it takes an infinite amount of energy to accelerate something from below the speed of light up to the speed of light. So you can't make a tachyon by accelerating normal matter.

The possibility of tachyons pops out of the mathematics of relativity (in a similar way that Dirac saw the possibility of the positron in the mathematics of the electron). The difference is that positrons were rapidly found, while tachyons have not to date, despite several experiments looking for them.

In relativity, there are multiple places like time & length with factors like 1/√(1-v^{2}/c^{2}). This approaches infinity as v→c.

It becomes "imaginary" if v>c, which leads to the possibility that it is not a realistic solution.

However (in my primitive understanding), despite the unreal nature of time and space for such particles, the equation for energy comes out as a real value, which has held out the tantalising possibility that these *may* be real particles.

How you could create or detect them is unknown, but that doesn't stop people from trying...