Red Chasm is the eighth level in Challenge Mode for Pikmin 2. This place has one of the largest populations of Dwarf Bulborbs and Red Bulborbs in the game, so it could be hard to get a Pink Flower.
Strategy
Try Finding the Bulborb that has The Key. Resetting will be helpful here. Take out all Bulborbs in the path back to the Research Pod, making it easier by simply luring the Dwarf Red Bulborbs away. Although there is no need to do so for a Pink Flower, you can collect other treasures if you have time by defeating the Bulborbs.
Using Ultra Spicy or Ultra Bitter Spray can help a lot in defeating the Red Bulborbs, particularly if you can hit two at once with Ultra Bitter Spray. Also, always make sure you can hit them from behind. The Dwarf Red Bulborbs shouldn't give you much trouble, but try to keep track of your Pikmin while they are around, especially if your aim is a Pink Flower.