Step one: if you're planning on doing something "not exactly legal" in your jurisdiction never SAY that on an open forum. Instead ask how would one theoretically remain as anonymous as possible.

Step two: always remember Bitcoin anonymity exists on a continuum from zero to nearly perfect, but never perfect. The higher the scrutiny expected the more careful and knowledgeable you must be.

Understand all Bitcoin transactions are linked, meaning if your identity is exposed in one place it can potentially be linked to coins any number of transactions away. So you need to think in terms of "believed safe & anon" vs "linked ID" zones. Ideally you use separate devices for the two categories and safely mix or clean coins between them. Get something wrong, the smallest slip up, and your ID is potentially compromised.

That being said it's not hard to break ID links, because many services let you deposit and withdraw bitcoins anonymously, using just an email (if that). The exchange BTC-e.com is an example. So first you should set up an anonymous email. Tip: if you're not using Tor or an anonymous VPN etc. then registering with an email provider (or visiting any site) isn't exactly anonymous. Your IP address is likely logged. Once you have your anon email send your linked ID coins to a BTC-e account, for example, then withdraw them to another service, like a Bitcoin casino/gambling site. From there withdraw the coins to an online wallet you've set up anonymously, like block.io. And from there send the coins anywhere you want, like an anonymous Nucleus account. By depositing and withdrawing coins with large services it's unlikely you'll get back the same exact coins you deposited, and doing this in multiple steps is basically guaranteed to break all original links back to you after a while. You just need to do the transfer work and be careful of mistakes. Best of luck.