A World Medal is an item in Super Monkey Ball 3D. These appear on the world select screen and show that you have done a particular achievement.
If you collect a 7 of each medal, you will get two special collectibles.
Note that these medals are pureley asthetic and do not affect the gameplay.
These two are the easiest to get. In order to recieve them, you must collect every banana on the bonus stage. There are two of these per world, and the one recieved will be determined by the control setting. You get a red medal for using the circle pad and a blue medal for using the motion sensor.
Collecting seven of each medal will earn you the World Master collectible.
In order to recieve thi medal, you must collect every banana in every stage, all in one run, without using a continue. While this is not incredibly hard, it still can be difficult in some stages, due to the layout. Note that collecting the banana collectible is not required (since doing so in some worlds would make it impossible to earn other bananas).
Collecting sevel of this medal will earn you the Banana-phile collectible.