The mice must wait for the shaman to act, grab the cheese and run back to the hole on the left platform as soon as possible.
They need to be careful though, because the bridge is bound to break either by the weight of the mice, or by the shaman trying to build to the cheese.
The shaman starts with the mice on the left platform, and must add weight to the bridge in order for the mice to reach the cheese.
Place a red-anchored plank right underneath the cheese.
Another, infamous technique of clearing this map as a shaman is to first tell your team of mice to wait on the platforms (use arrows) and then use a cannon ball to destroy the bridge. Then build a ramp or a bridge to the cheese and back. (If there are some mice who are on the other platform, you of course needs to build the ramp/bridge a little bit more).