Volitions do not enter into the chain of causation…. The feeling that we call volition is not the cause of a voluntary act, but the symbol of that state of the brain which is the immediate cause.
– T.H. Huxley
The experience of willing an act arises from interpreting one’s thought as the cause of the act.
– Daniel Wegner
Free will is an inherently silly concept. It's not something that has to be "disproven", because the idea doesn't even make sense in the first place. It doesn't matter if the universe is not deterministic, it doesn't matter if our brains could use quantum effects to introduce uncertainty into behavior (by the way, they probably can't).
**Assumption: I'm assuming that by bringing up "tachyons", a theoretical particle that sci-fi sometimes uses as a buzzword for things involving time travel, the questioner is really wondering about whether or not knowing the future disproves free will.
To talk about Free Will, we first have to define it.
First though, let's talk about what free will is NOT. Free will is NOT simply "having the ability to do what you want to do". This is called "freedom of choice", and it is irrelevant to the discussion, because tachyons, determinism, and quantum physics have nothing to do with it. Of course you can do what want, unless something outside yourself stops you. Knowing a predetermined future wouldn't get in the way of that. If you could see the future, you'd see that you did whatever you'd want to do given that you know the future.
The definition of Free Will most philosophers use is the Cartesian one. "Given the exact same situation, could you have done anything different?". If not, then you are said to not have free will. But let's think about that for a second. Did you choose to do whatever you did for some reason? If so, then given THE EXACT SAME situation again (same brain state, same memory, same situation), OF COURSE you'd choose to do the same thing again, for the same reason you decided to do it last time. On the other hand, if you DIDN'T do it for a reason, then it means you just did it randomly. Taking random actions is not really what I think people want when they are worrying about free will. Doing things randomly doesn't give you agency, it turns you into a glorified coin flip. Given this perspective, do we really think it matters if the universe is deterministic? If it's not we're dice, and if it is we're clockwork. Neither one really addresses the existential angst that people tend to feel over free will.
Even if you believe we have souls, it doesn't fix the problem. So what if you have some kind of magical ethereal mind in hammerspace that can influence your biological brain? Does your magical ethereal mind do things randomly? Or does it make decisions based on reasons? If it's reasons, then your soul is ALSO clockwork. If it's random, then your soul is just magical ethereal dice.
Free Will is a red herring. It's not something that actually matters, or even makes sense to want. You are clockwork. Or maybe sometimes you are dice. Neither is very satisfying.