I believe Uber is massively overvalued and it will face down rounds in the near future. Assuming I can use all financial instruments, how could I short Uber?
The answer to this question is related to another question:
How would I invest in Uber?
Given that Uber is a privately-held company, the average investor cannot directly buy stock. However, there are some indirect methods that you can use to invest in Uber, and as a result, it is also possible to indirectly short Uber.
One method is to invest in (or short) companies that invest in Uber. Alphabet/Google (GOOG) owns some, as well as Microsoft (MSFT), Toyota (ADR), and other companies. Theoretically, you could short these companies, as a hit to Uber would be bad for those companies.
Another method would be to look at Uber's competitors. Think about what companies would do well if Uber went under. Lyft, perhaps, although it is so similar to Uber that if one has trouble, the other may as well. Perhaps instead you might invest in a traditional taxi company, or a company that provides services to taxi companies, such as Medallion Financial Corporation (MFIN).
Keep in mind that either investing or shorting any of these is not really the same as investing/shorting Uber. It provides you some exposure in Uber, but your investment is also affected by many other things that have nothing to do with Uber.
For more information, see the Investopedia article Ways to Invest in Uber before It Goes Public.
For the record, I don't recommend that you do any of this.
Pay someone a fee to borrow their private Uber shares, then sell those private shares to someone else, then find someone else you can buy their private shares from for less than the net of the proceeds you made selling the borrowed shares you sold plus the fees you've paid to the first person and return your newly purchased shares back to the person you initially borrowed the shares from.
On a serious note, Uber is private; there is no liquid public market for the shares so there is no mechanism to short the company. The valuations you see might not even be legitimate because the company's financials are not public. You could try to short a proxy for Uber but to my knowledge there is no public "rideshare"/taxi service business similar enough to Uber to be a reasonably legitimate proxy.