That is sometimes crashes the browser probably can't be helped - the MS JVM is very old and buggy.
You can run the applet offline and profile it like any other
Java application, something like the following:
java -classpath C:\j2sdk1.4.2_04\lib\tools.jar -prof sun.applet.AppletViewer appletpage.html
That will produce a profiling file that can be analyzed with any number of tools, e.g
ProfileViewer, if I may advertise a tool I worked on myself.