It's basically your mama wombat against the dingo in a race to save your babies. Here's the excerpt from the rulebook:
Solo Game Rules
Wombat Rescue can be played solo with just a couple tweaks to the rules.
When setting up the playing area, make sure 1 of the terrain tiles with a dingo den space is roughly the same distance away from the baby wombat tiles as the home tile. This is the starting den for the dingo.
You can use your tough wombat hide to ram into the dingo and chase him all the way back to the starting dingo den space. This means that if you run into the dingo during your movement phase, move the dingo immediately to the starting dingo den space. If you are carrying a baby wombat, he must flee back to the space where you found him. However, you do not have to flee back to the home space.
You will move dingo every turn during your cleanup phase, but not until you have 2 poop cubes out on the playing area. Roll the dingo die a number of times equal to the number of baby wombats you have rescued (minimum of 1 roll) and move the dingo after each roll. The dingo becomes more and more agitated with each baby wombat you rescue and he moves much faster! In the solo game, the dingo will always move toward the nearest baby wombat!
You win if you manage to rescue all of your baby wombats. If the dingo catches any baby wombat by himself before you can rescue him, you lose. Try again! If you find the solo game too easy or too difficult, try varying the position of the starting dingo den.