This is for the third special mission that you have on the Ranger Web. Mew follows a specific pattern in how it travels and this pattern repeats.

1. The first place it appears is the place that has the bridge.
2. The second place it appears is to the North West where there are a bunch of vines to climb, right before the hole to go into to catch Gyrados in on of the earlier missions.
3. The third place is to the direct East of this place. It is the place with lots of water that you can walk across. You see Lotad there.
4. The fourth place is the path between place 1 and 3.

Hope this helps.