Punky Plum and Punky Turquoise
or SFX Pimpin Purple or Deep Purple Adore Purple Rage
Adore Aquamarine
Honestly, I don't know about punky colour, but if you're in Europe I'd avoid directions plum and turquoise as the new formula for both is stainy and has a weird fade.
That pic is photoshopped, in real life it is much harder to get those types of colours that are vivid yet muted at the same time.
I would bleach to an orange/ gold shade, then use something like Midnight Blue for the teal and Rose Red or Cerise with a dash of Midnight Blue for the pink/purple side.
Don't know about the purply side, but the teal side looks a lot like a mix I did with Stargazer blue black and tropical green in a 50:50 ratio, no diluting. It looked like this :
Tropical green on it's own is lighter and more green. The added blue makes it teal. I've never had any issues with Stargazer fading too quick on me, but I know others can have problems with longetivity.
I would try pravana wild orchid and directions alpine green/manic panic enchanted forest
this is me a few months ago, and mine is not photoshopped. looks pretty similar. half sfx pimpin purple, half sfx sonic green over a (much faded) pink base.
eta another pic--