Chakra nature of Tailed Beasts
A few facts first:


Kurama's chakra isn't healing type. Minato sealed Yang-Kurama in Naruto, which resulted in the chakra Kurama gave him to be Yang oriented. This adds the healing properties to that chakra.
Not all tailed beasts have a known nature, but some do.


So the natures:


Shukaku - Wind, evident by the Drilling Air Bullet he fired at Gamabunta.
Matatabi - Fire, evident by the fireball she fired at Hidan and Kakuzu when they battled her.
Isobu - Water, obvious.
Son Goku - Lava (Earth and Fire), evident by multiple lava techniques reanimated Roshi used while in Jinchuuriki form.
Kokuo - Not revealed. His Jinchuuriki was said to use the Steam element (Fire and Water)
Saiken - Not revealed. His Jinchuuriki uses Water element and specializes in bubbles. Saiken himself was shown to be able to spit acid.
Chomei - Not revealed. Not much was revealed about its Jinchuuriki too.
Gyuuki - Not revealed, but presumed Lightning. His Jinchuuriki uses Lightning.
Kurama - Not revealed, but presumed Yin-Yang. His Jinchuuriki was shown to have remarkable stamina and healing properties, which suggest Yang nature which is compatible with the half of Kurama he had. The other half's chakra was not explained thoroughly.
Last but not least


   Shinju (God Tree; Juubi) - Natural Energy and Yin-Yang. Evident by the techniques Obito uses after becoming its Jinchuuriki, as well as what was revealed in the manga.