How to complete the Turffield Gym mission
As soon as you enter the Turffield Gymnasium, you'll be faced with a challenge that requires you to take groups of 20 Sheep at a time and lead them to the bottom to get past each barrier. The first of these is very simple, because you are walking right behind them and they will be heading towards it. They may be separated, but take your time and you will lead them all to the barrier.
As soon as you get them at the barrier, you will meet Gym Trainer Samuel whom you will have to fight. All he has is a Gossefleur, so make it easy and move on to the next part.
Once you get to the second area, you'll have a little more trouble thanks to two obstacles. The first is a Voltoutou that scares the Moumoutons in the other direction, so that your Moumouton party can split up, which is a search. You just need to group them together if necessary and sneak into the area that the Voltoutou is not.
In addition to the Voltoutou, you will meet Mark, the gym trainer, who is more in the way than Samuel was. Mark has a Rozbouton and a Mystherbe, which you should be able to do quickly with character combinations. You can even skip this match if you move Sheep enough.
You've now made it to the third and final area, which has two Yampers to dodge and a trainer to fight as well. You'll probably have to separate the Woo Loo here at some point, but it shouldn't be too hard to go through. Gymnastics trainer Leah will challenge you on your way by throwing Croquine and a Mystherbe.
Once you have defeated Leah and the 20 Sheep are completed by the end of this third zone, you will have completed the mission and can face Milo, the manager of the gymnasium.