this is a good question; because, it leads to examples. I’ll start right away, then leave comments.
Hawk: The lake towns are rich hunting grounds; I will not allow a few mice to unsettle my nesting
Mice: The lake towns provide many resources; we will prevent this predator from disrupting local commerce [by killing it | by unsettling the nest]
Results (if mice win):
Minor Comp (two possibilities): We’ve won; the hawk’s nest has been dumped from the tall, lonely pine; unfortunately, several merchants feel insecure and want Guard escorts–in wholly different directions. It will be nearly impossible to offer our duty to all of them this season. OR We’ve won; the long hunt ended with the death of the hawk; unfortunately, weeks of harvesters hiding out of sight has caused a serious shortage of grain and fruits. It will be a challenge to gather enough forage for the towns to last next season.
Comp (two possibilities): We’ve won; the hawk will seek a nest elsewhere, but we’re all tired from the hunt and the lake town mice don’t feel any safer. Commerce and harvesting may suffer while mice don’t believe they are safe enough to go above ground. OR We’ve won; the hawk is seriously injured, but our patrol leader is injured and we all are tired. How can we serve other duties while our Patrol Leader needs to recover?
Major Comp (two possibilities): We’ve won; the hawk’s hunting grounds are marked for lake town residents to be safe; unfortunately, we’re all injured and tired, and worse, the lake town mice don’t trust us to solve the problem. We’ve got to rebuild relationships and trust in the Guard. OR We’ve sorta won; the hawk is still a serious threat, and we’re all hungry; however, we’ll be able to escort the merchants of the lake towns safely. We can’t rid the Territories of every predator, but we can minimize the danger.
Of course, we could look at examples of results if the hawk wins, but I’ll have to save that for another comment.
First facet, don’t think of the goal as the animal’s actual thinking. Do think of it as a general sense of instinct.
Second facet, don’t make or allow players to make goals that are directly opposed. Make goals that are askew; they are moving in roughly divergent directions, but cross each other. The conflict occurs, then the compromise reflects how the path is distorted after they meet. Directly opposed goals are like head-on collisions or at the very least like playing chicken.
Third facet, look for surrounding factors that matter to the story. If a friend or enemy is nearby, draw them into the circle of conflict. If settlement mice are going to see or hear the conflict or the results of it, it had better cause a ripple effect through the settlement(s). If the patrol is not struggling to fulfill duties or mission objectives, drive the compromise to place an obstacle to such completion.