From this room, instead of falling to where Mecha Birdo was:
(http://img.photobucket.com/albums/v69/One_Alternate/iwbtgvinescropped.jpg)
I went through and got the thing that looks like a gun handle in the top right (though I haven't noticed any difference in my shots.)
Then from the elevated square where it was, I double jumped over the wall to the upper right, which seemed natural as it was similar to the way I got to this room in the first place.
Then, moving right, I would fall off of that wall, and I would fall through several scrolling black screens until my character disappeared (no game over screen.) But if I held left to hug the wall, then fully double jumped to the left once the wall ended, I would land on the wall seen in the first post.
Above that screen is a green diamond high up on the screen and a design that looks like fireworks below the diamond and to the right.
Below that screen is the rest of Mecha Birdo, and far below that is a single gray tile I can stand on but doesn't seem to do anything.
I can shoot parts of Mecha Birdo as I fall, and it makes sounds when hit, but even with the maximum number of hits on any part that responds, nothing happens.