Because the tips are hot pink instead of just purple over blue your options are to start with a white ponytail wig and dye it to that gradient. Dye the blue part first with the colour saturation fading where the purple should start, dye the purple over the blue fade and fade the purple out, then dye the hot pint over the purple fade to the tips.
I recommend the FW inks for this.
Or you happen to have a airbrush and "paint" the tips that hot pink over a blue wig with thinned out luqitex acrylic paint thinned out to use in the airbrush.
Another route is to not dye at all but to layer the coloiur in.
Base wig in teal
Clip-on in Hot pink as the base
1 Grape wefts to sew onto the hot pink cliop on's
2 Teal Clip-on or 2 long Wefts. to sew over the grape hot pink clip on you made
You will need to layer the hair so that the color gradient is noticeable.
If you want them to be poofy. Instead use all long wefts and make a pillow in a similar hot pink shade to use as a base. You then sew thw wefts to the pilloe int tha layers look starting at the bottom and work you way to the top teal. Again trim the layers in the hair so that you can see the gradient.
Also when working with long hair you want to pre-treat it with silicon spray so that it doesn't tangle horribly.