Change Swimsuit:
At Event Selection screen, highlight 100m freestyle and press Up, Up, Down, Down, Left, Right, Left, Right, Circle, X.

Space Shuttle:
In the Pole Vault, clear qualifying height (4.5 m) on first attempt. On second attempt, clear 5.0 m. On the next turn a space shuttle will fly by.

T-Rex:
In the Shot Put, get a distance of all the same numbers (55.55, 22.22, etc.). A T-Rex will visit the stadium.

UFO:
In the Javelin, tap the run button once. As soon as you see the angle meter appear press and hold X to get above 60 degrees. When the meter rises start pressing the Square or Circle button rapidly. The javelin must be thrown with the maximum power at an angle of more than 60 degrees. A UFO will fall into the stadium with the javelin protruding from it.

Thanks to Revolution readers Ajay Ramtohul, Paul Doran, and Mike!