First, go to Editors > Upload a video: http://www.animemusicvideos.org/members ... upload.php
Choose the video you want to request the upload for and click on "request upload permission".
So far so good, it's the usual upload request you've always done.
Now from this page, if you scroll, you'll see a link to the request large upload form, which is this: http://www.animemusicvideos.org/members ... -large.php
Fill out, send, pray. That's about all I can do for you on the matter, unfortunately.
Of course, one thing to keep in mind is that the free user limit is 150 MB, and the donator limit is 300 MB... so if it's under 300MB donation would be an easy way out.
I'm not sure how long or how detailed/actiony/high framerate your video is, but assuming it's feasible, perhaps working a bit on the compression could get you under 150MB? The filesize limit was put in place exactly due to that to begin with.