The best essential oil for dark spots is Tea Tree oil which I find works great for removing dark spots on my skin.
I first dilute the Tea Tree oil with some olive oil and then apply it to the dark spots everyday and then after 2 weeks the dark spots start to disappear and within a month the dark spots are completely gone.
Some other good essential oils for removing dark spots besides the Tea Tree oil is Frankincense Essential Oil, Lavender Essential Oil, Carrot Seed Oil, Cedar Wood Essential Oil and Helichrysum essential oils.
Just apply either of those essential oils to the dark spots and they should begin disappearing soon afterwards.
You'll just need to keep at it to see results but the dark spots will eventually fade and go away.