Changes

Emerald 1: This is 45 degrees to your right, similar to the ideal emerald 3 in mission 1.  However, it's further back and thus takes more time to get (3.50 seconds is the fastest known time for a straight run to the emerald).  A trick unique to Security Hall can be used to shave off time.  Rather than going all the way to the far-right corner and diving, do a dive into the near-right corner and press right so that the fan's upward boost is blocked by the floor.  This will lead to your death as you fall back down (or, better yet, dive down).  Now why would you want to do that?<br>

Emerald 1: This is 45 degrees to your right, similar to the ideal emerald 3 in mission 1.  However, it's further back and thus takes more time to get (3.50 seconds is the fastest known time for a straight run to the emerald).  A trick unique to Security Hall can be used to shave off time.  Rather than going all the way to the far-right corner and diving, do a dive into the near-right corner and press right so that the fan's upward boost is blocked by the floor.  This will lead to your death as you fall back down (or, better yet, dive down).  Now why would you want to do that?<br>

Remember that when you die by getting hit, you enter an uncontrollable death animation.  But when you die by falling through the kill plane, you maintain control of the character for a brief time.  Also importantly, once your death is recorded, the clock stops.  So the goal here is to intentionally die as fast as you can, and then you have about 2.5 seconds to freely move around with the clock stopped.  Normally there isn't much you can do in that time after falling through the kill plane, but this is Security Hall.  The emerald is a bit ahead of and above you, and--how conveniently--the fans are still there to blow you back up.  The fixed position of the camera during this time makes it very difficult to aim your course up into the emerald properly, but it can be done, and you'll likely get a time for this segment of less than 3 seconds.

Remember that when you die by getting hit, you enter an uncontrollable death animation.  But when you die by falling through the kill plane, you maintain control of the character for a brief time.  Also importantly, once your death is recorded, the clock stops.  So the goal here is to intentionally die as fast as you can, and then you have about 2.9 seconds to freely move around with the clock stopped.  Normally there isn't much you can do in that time after falling through the kill plane, but this is Security Hall.  The emerald is a bit ahead of and above you, and--how conveniently--the fans are still there to blow you back up.  The fixed position of the camera during this time makes it very difficult to aim your course up into the emerald properly, but it can be done, and you'll likely get a time for this segment of less than 3 seconds.

Emerald 2: Follow the Mission 3 path up to the top.  Rather than stopping at the B symbol for the spring, though, just run forward to the laser complex.  Do a short jump over the first laser, then after landing do another full jump while holding forward.  This can launch you up into the beetle enemy, and hitting it gives you an upward boost that allows you to glide forward to the emerald.  This segment should take a bit over 13 seconds.

Emerald 2: Follow the Mission 3 path up to the top.  Rather than stopping at the B symbol for the spring, though, just run forward to the laser complex.  Do a short jump over the first laser, then after landing do another full jump while holding forward.  This can launch you up into the beetle enemy, and hitting it gives you an upward boost that allows you to glide forward to the emerald.  This segment should take a bit over 13 seconds.