I didn't realise this game both had a forum and my run submitted to it.
I see that I'm listed at 4th place on Wii U, even if my time is the lowest. I guess it's due to Real Time missing. I didn't submit it to speedrun.com myself, but it's on SDA. What's needed in order for it to get a RTA time?
The info on the SDA page (with my timing back then) says it's 34:42 (see http://speeddemosarchive.com/DuckTalesRemastered.html).
Edit: I notice your timing is different than back in the days. I confirm difficulty 5 seconds earlier than the actual gameplay starts, so RTA timing should be 34:47.
Edit 2: Also, how do I claim that run to be mine?