Depending upon how you want your mechanics to work and feel, True20 can very easily and elegantly do Sci-Fi with no effort at all, or it can be a rampaging siberian bear that never goes where you want it to.
If you want separate, distinct mechanics for each of those areas then you'll be disappointed. You'll need a couple of different supplements to get even halfway there, and you'll have to invent the rest.
On the other hand, if you're willing to reuse a number of mechanics then you'll quickly find yourself done with only a little bit of work and most of that being flavor text.
Advanced Weapons: given that laser weapons are already in the system, this requires almost no effort at all. There are enough listed weapons of enough different types and power levels that you can quickly get a feel for where your favorite super-gun should fit in. Powerful as a modern tank cannon? Ten damage. Powerful as a tomahawk cruise missile? Fifteen damage. Easy.
Advanced and Prestige classes: Feats. There are only three roles (and roles are different than classes, though it's difficult to see how initially) but the abilities of the character are defined by their feat choices. Anything that can't already be produced by the existing True20 rules (and there isn't much) can generally be distilled into a feat or maybe even a few feats that define the prestige class; decided on appropriate prerequisites and you're done.
Starship and Mecha/vehicle combat: Depends. I like to think that I've built a great system for starship and vehicular combat (thanks for the pimping, Dragon-Slayer) but I'm a bit biased. Alternatively, you can run them just like a character combat and you shouldn't have much trouble. Finally, you can invent your own method if you don't like any of the other options available. It's not too difficult once you have a basic idea of how you want things to work.
Battle-suit mechs (even the ones from Battletech) would work just like character combat. Use the mech's combat modifiers (including Toughness) instead of the pilot's for most things. Heck, you can even use both at the same time (poor humans are gonna die).
Flexibility: The system will run just about anything, from
dreamscapes shaped by whim* to the most historically accurate adventure you've ever wanted to run; and it will do most of this as well or better than any other system you can find. It will do the science fantasy of Star Wars or the hard science fiction of [... mind blanking for examples].
Cybernetics: This is where a desire for distinct mechanics will become a serious problem. If you want separate mechanics for cybernetics then I would recommend looking into True20 Cybernetics (which can be purchased
here) or poking through the True20 forums looking for cybernetics systems (which you can start doing
here).
Personally, if I didn't just want to use cybernetics as replacements for lost body parts (which is what early cybernetics are always for), then I'd probably want them to provide benefits similar to some of the True20 powers. In that case I'd just write up a simple feat that let you acquire a cybernetic component that gave you the benefit of a power at a certain rank; cyber-adept (the Adept role) would allow you to push these components beyond their design limits, allowing you to use your adept rank or the implant's rank, whichever was higher.
Damage: The damage system is both like and unlike the latest edition of Shadowrun. There are separate tracks for lethal and non-lethal damage; non-lethal can potentially wrap around into lethal damage; lethal damage always inflicts the equivalent non-lethal condition in addition to it's lethal component. There is a bit of a death-spiral effect, where past damage makes future damage more likely and characters can easily be stuck in a loop of inactivity (unless they spend their heroic resource to act anyway). However, there is no survivability limit: a character can (theoretically) take an infinite number of tank shells, or go down to a single swipe by a house cat; it's all a matter of luck, toughness and whether or not the character has any heroic resources (Conviction) left to spend.
Overall: True20 can do what you want, and do it well and easily. I'd recommend picking up the hardcover, despite the lack of an updated printing. It comes with four example settings in the back, two of which are sci-fi (Japanese mecha and operatic science fiction), that make it worthwhile to put up with the flaws.
Good Luck!
*Sorry for the link, but I had trouble finding a simple summary of Nevermore that didn't require money to read. A free pdf product was the best I could do. My apologies for a probable violation of forum policy and general rudeness.
