We're working on a guide for people to invest anonymously with us. It's not so simple. Monero is great, but their current defaults are too low to guarantee the privacy they say they have, and changing the defaults makes your transactions stick out.
What you have to do is:
1. Exchange into Monero.
2. Churn with Monero. This means you'll send your XMR from your wallet to your wallet, over and over again. Probably once every 3-6 hours, randomly. The destination address is private in Monero, so sending to your own wallet is fine.
3. After some time (1-3 days) send to another exchange to get Bitcoin/Ether/etc. Need to look at trade volumes to make sure you don't stick out. And probably not send out the same amount you put in. Keep half or some chunk and slowly leak it back to Bitcoin.
4. Optionally one could stack on a couple of Bitcoin mixers, on the idea that you won't have the bad luck to hit two compromised mixers. But each one will take ~2% so it adds up.
At that point you have coins reasonably unrelated to your earlier identity. Getting them into cash is a whole other guide.
If you say, split up the ETH and tumble it into a number of smaller wallets, transfer it to BTC with a bunch of seperate accounts and/or exchanges, and then tumble it again on the BTC side, then it no longer is as simple as requesting one transaction from one account.
Now you have to trace the currency through the tumbler, request information on n number of accounts while providing details indicating that all n accounts are tied to some crime, and then trace all of said currency through another tumbler.
At this point, if it all ends up into one BTC wallet, you could find them. However if it ends up in a number of smaller BTC wallets, you also have to now prove that those wallets are all owned by the same person and not just a bunch of wallets owned by seperate people who happened to have a total of x amount of BTC adding up to roughly the equivalent value in ETH minus transaction fees.
It goes from one step with some paperwork into months worth of work by a team of skilled people, a tonne of paperwork, and a high probability of ending up with a dead end after all of this.
This could be considered handling stolen goods, and could be prosectuable. Anyone who has access to the private keys that have been involved could potentially be considered an accessory (provided they have spent them and not reported the transaction).
A lot of the online exchanges are government-regulated nowadays though, and require photo ID for you to be able to do things. Mind you, it should be fairly trivial to forge or use stolen IDs. I think Coinbase asks for a second ID at one point, probably for larger transactions. But either way, those will have a transaction log, so they can see the path from wallet > fiat > bank account, and from there the banks, also regulated, can point to you (and they do / should check your ID with a bit more scrutiny).
TL;DR it's only untraceable if you can do the exchanges between cryptocurrencies and to fiat in real life with shady characters.
Has been a thing for a few years now - https://localbitcoins.com/