Quote Originally Posted by Magus of Zeal
To get the Amazing Chocobo, your four Choco-Runners need
to be level 5. Simultaneously.
You've done everything else, this is the only thing you are missing. Get four of your chocobos that are at level 5 and make them the runners. If you don't have four, you need to find another one.

Quote Originally Posted by Magus of Zeal
Once you've completed both tasks, {addendum: leave the Chocobo Ranch and re-enter it, and} Clasko will discover the entrance to the
secret chocobo dungeon, in the Ruin Depths of the ranch. The full walkthrough
for this section is listed in chapter 5, as it's necessary to complete to get
100%. Enjoy!
That has driven many a person who has played this game a tad crazy.