IH8YOU explained it to me via PSN messages. I'm still not entirely sure on some of the details but will attempt to summarise here.

He was signed in and connected to online the whole time (I think).
He went into Racebox and performed a complete TT on Tech de Ra. (He had only got it to work on Venom and Phantom when I last messaged him)
He went back to the main menu and hit X over online, but hit O to go back straight away, without getting to the online menu screen.
He then went back into Racebox and selected Time Trial. He mentioned hitting select and X and almost the same time. If you hit select just after X when selecting Time Trial then it doesn't seem to bring up the online friends box that it usually would.
As far as I understand it, from there he just hit X all the way and it took him to Syncopia.

I think that's it, but he can correct me on anything that was wrong. I don't recall hitting the select button when it happened to me. It may just be coincidence, but he has done it more than once so maybe if people try that method a few times then they may have some luck.