To get past the first major test (Explorer), you simply need to access a page over IPv6, and pass a quiz. To do this, spin up a desktop VM on your dual-stack vn-segment and navigate to https://ipv6.he.net/certification/
To get past your next phase (Enthusiast) you do have to spend some money - purchase a domain (the cheaper, the better) and link it to he.net's name servers. Jacob Salmela has a pretty good step-by-step on this: (https://jacobsalmela.com/2013/10/30/ipv6-certification-walkthrough-enthusiast-level-hurricane-electric-part-3/)
From here, you should be able to get through it via trial and error. I recommend just spinning up a linux VM on that vn-segment and toying around with it, e.g. installing apache, postfix, etc.
One thing worth noting is that the last few phases (Professional on up) have automated tests that may need to be manually restarted by HE to work. If you get really stuck, you can ask them at email@example.com.