Either there's a bug that makes it slow or your code and or how you've done it is making it slow. It also depends on what you're using, basic java and java2d or LWJGL or LibGDX.
If the things that you're doing (effects or whatever) are being done smoothly by other similar applets then you might consider why that is and how you could make your code more efficient.
Using OpenGL libraries like LWJGL, LibGDX or JOGL allows you to take advantage of the graphics card and make rendering a lot faster. This comes with a longer loading speed (loading speed doesn't really matter anyway) and more disciplined rendering/programming practices.
Is there anything I can do to make it run ok in the browser, rather than paring down the code or making it more efficient?