For the best times, immediately run down the left side and jump when about a mouse-width from the bottom. It is important to not jump again while running up the second slope, because this will compromise speed. Run up the right slope and leap towards the cheese when at the same elevation as the cheese. Carefully land, run down and jump left. While running back up the left slope, the best strategy is to hold left and mash the up key at the same time.
Because of the weight of the cheese, running uphill with it will cause your mouse to run in place.
If unaccustomed to the controls and you are just aiming for the cheese rather than being first, wait for the Shaman finish building if they intend to build anything.
If a shaman tries to drop anvils on you, you can run right from the anvils and jump back up. However, Boxes or anything larger in mass than an anvil will take you down. If the shaman starts to do this, you can wait and they will probably stop.
The Shaman can assist mice by bridging the gap in the center and/or building a structure to the cheese.
The center can be bridged by carefully sliding, running up, and globally anchoring a large plank across the gap before sliding down. Alternatively, certain contraptions, such as a + or T shaped structure, can be launched down the slope and fall in a way that bridges the gap. Take caution not to kill or trap mice in the process of creating the bridge. You can also create an anvil swing to the middle, drop a long plank on the gap, then stand on it and anchor it with a ghost red short plank so it won't slide into the hole.
A bridge can be made to the cheese from either the left or right side. It is best to begin with a globally anchored transparent plank placed alongside the ground, and then yet another transparent plank anchored to that. A solid plank can block mice; therefore a smaller plank anchored to the second one should be placed to continue the bridge. Remember to leave a gap for the mice to get through.
A simpler method is to add a globally anchored plank underneath the cheese, making it easier to jump to.