Is it possible to win the boomerang game near level 2 with the normal boomerang? After the second hit, I'm already too slow.

Do I need to find the ladder for level 2, or is there something else I'm missing? I have a key, but the only locked door I can see is in the room with the compass.

Edit: Never mind, found the ladder. Stuck near the end of level 2 though. I'm missing a key to get into the last couple rooms in the lower section. The only other room I haven't gotten into is one near the east end of the upper section. There's a closed door in the room to the west, but I haven't found a way to open it or any other way into that room.