This can be done using Java Agents and an instrumentation library.
Java agent - Separate code that can be made to run before the main part of the code.
Instrumentation - Changing the source code during the load-time of a program.
Code for making it work
(taken from appcrawler and modified slightly):
The agent.jar source code:
SimpleTransformer.java:
package test;
import java.security.*;
import java.lang.instrument.*;
import java.util.*;
import javassist.*;
 
public class SimpleTransformer implements ClassFileTransformer {
 
  public SimpleTransformer() {
    super();
  }
 
  public byte[] transform(ClassLoader loader, String className, Class redefiningClass, ProtectionDomain domain, byte[] bytes) throws IllegalClassFormatException {
    return transformClass(redefiningClass,bytes);
  }
 
  private byte[] transformClass(Class classToTransform, byte[] b) {
    ClassPool pool = ClassPool.getDefault();
    CtClass cl = null;
    try {
      cl = pool.makeClass(new java.io.ByteArrayInputStream(b));
      CtBehavior[] methods = cl.getDeclaredBehaviors();
      for (int i = 0; i < methods.length; i++) {
        if (methods[i].isEmpty() == false) {
          changeMethod(methods[i]);
        }
      }
      b = cl.toBytecode();
    }
    catch (Exception e) {
      e.printStackTrace();
    }
    catch (Throwable t) {
      t.printStackTrace();
    }
    finally {
      if (cl != null) {
        cl.detach();
      }
    }
    return b;
  }
 
  private void changeMethod(CtBehavior method) throws NotFoundException, CannotCompileException {
    /*if (method.getName().equals("doIt")) {
      method.insertBefore("System.out.println(\"started method at \" + new java.util.Date());");
      method.insertAfter("System.out.println(\"ended method at \" + new java.util.Date());");
    }*/
    
  
          //MY CODE
      //!Modifier.isAbstract(method.getModifiers()) -- abstract methods can't be modified. If you get exceptions, then add this to the if statement.
      //native methods can't be modified.
      if (!Modifier.isNative(method.getModifiers())) {
          String insertString = "System.out.println(\"started method " + method.getName() + "\");";
          method.insertBefore(insertString);
      }
  }
SimpleMain.java:
package test;
import java.lang.instrument.Instrumentation;
public class SimpleMain {
  public static void premain(String agentArguments, Instrumentation instrumentation) {  
    instrumentation.addTransformer(new SimpleTransformer());
  } 
}
MANIFEST.mf:
Manifest-Version: 1.0
Boot-Class-Path: javassist.jar
Premain-Class: test.SimpleMain
Take these files and package them into a jar file. Also make sure to include files from javassist.jar (downloadable from www.javassist.org) and tools.jar (found in Program Files/Java/jdk/lib/). Not sure if the second one is necessary, but the article says it is for some reason.
Now you can use this jar file as a java agent.
java -javaagent:agent.jar YourJavaProgram
And voila. The java agent will instrument all methods and print out every method called during execution.