I've been searching for how to solve slowdown on paper effects on TTYD by that I mean building the bridge in the first chapter and Bowser breaking through his castle. I am using the newest version of Dolphin and i'm on Direct3D 11.
There's no solution. The effect is done in software and is not hardware accelerated by the GPU (yet).
Do not disable Bounding Box for Paper Mario games, it will randomly crash or softlock the game in various places. Are you running the latest development or beta version of Dolphin? Have you tried switching to Vulkan or OpenGL backend? AFAICT you'll only experience slowdowns during those effects when using super high internal resolutions...
The effect is done in hardware. We've had hardware bounding box for many years. It's just very slow even with hardware bounding box emulation. You may need to lower your graphics settings during strenuous graphical effects like these.