The most effective method of breeding a cactus dragon is a plant dragon (lv 10 left) and a lightning dragon (lv 10 right).
The egg will be green with a turquoise lightning bolt. It will take 30 minutes to breed, and 30 more minutes to hatch. It unlocks at level 11, and it gives 20,000 experience points when hatched. It can be purchased from the market for 500 gems.
Some other proven breeding methods are (listed left to right and level 10 unless noted):
Breed a Crystal dragon with a Cactus dragon.
Cactus Dragon and Rust Dragon
Either buy it for 1,425 gems or breed it using the cactus dragon and the crystal dragon in the breeding cave.
You don't breed a Kairos Dragon in DragonVale. You have to get parts to complete it.
You can only breed it in November and you need to breed cactus and firefly. The Breeding/Incubation time is 30 hours. You should check out the related link.
you breed a ice dragon with a mine dragon
Cactus and crystal i am told
You have to breed a plant and a fire dragon.
As of July 2012, there has not been a star dragon in DragonVale.
You have to breed a sun and moon dragon together
You have to breed a metal and a water dragon together.
You have to breed a plasma dragon with a salamander dragon.