Go to Hyrule, and have one character be Mario, the other be Samus, Link, or Young Link. Have Mario stand on the lower grassy part of the level (as shown in blue in the screenshot). At the left-most part of the level, have Samus/Link/Young Link grab the edge. Then press backwards (left in this case), press and hold forward (right), and then have the character grab (Z) on the little part of that thin platform (as seen in the screenshot - red indicates Samus/Link/Young Link). When the desired character grabs onto that little part of the level, have Mario jump and use forward+b on his opponent. The character will either go flying upwards, or will turn around and be holding onto nothing. It is possible that this sort of glitch will work just about anywhere, by having the character grab something and hang there (Like on a wall in Fourside, or near the edge in Final Destination).
Submitted by: Jesse