I've run attractmode on both linux and windows 7 on a p4 with a radeon 7500 vga video card with zero issues.
We are going to need more info about your setup.
What OS
what CPU
What video card.
I actually didn't think this was an unknown issue, seeing as how a quick Google search can find plenty of other people bringing up the problem, with the typical recommend "solution" being to personally downgrade one's videos, especially if they are over 30fps. For what it's worth:
Windows 7 64-bit, i7 980x, Nvidia GTX 1070. I access these files over USB2, but I've tried running everything off a local drive and get the same results, so that's definitely not it.
Here, a quick link to one of the videos I use:
https://mega.nz/#F!CgwzQJ5S!xysgH9Uydl0QJ9fXtqXriw (main menu video.rar). Try it for yourself (on PC). Watch it in AttractMode until you get to the part with the Link/King cartoon with the dialogue. On my system, in a media player, this part is in perfect sync, while in AttractMode it is by that point a full two seconds out of sync (video is ahead of the audio, due to dropped frames). If that's the same with you, then you now know what I'm talking about. If it's not, then maybe there is some hope after all. Some setting I've overlooked. The topic of hardware acceleration has been brought up many times here, but there is a lack of information. Currently it is assumed that the option is simply not available on the PC iteration, and its presence as an "option" is an overlooked redundancy. When I watch the CPU usage, one core gets 100% of the responsibility of processing these videos, and it gets capped out. That would certainly do it.
I'll add that probably most video packs out there are only 29.97 or 30fps, and certainly those play in AttractMode without issue because of the dramatic reduction in required CPU power. So if you discover that the above video gives you sync issues you weren't expecting, then at least you know the probable reason why.