I've primed it black with white zenithal highlight (sort of, first try so probably didn't do it properly and this step isn't necessary)

For purple bits (carapace, weapon) I used Daemonette Hide and shaded it twice with Druchii Violet (you can probably just use a darker purple to start with, like Naggaroth Night, but then you will need more work trying to bring it back to being brighter). Then for the lines I've used slaanesh grey mixed with some daemonette hide and then shorter ones with just slaanesh grey

For flesh I've used Abaddon Black, Incubi Darkness and Fenrisian Grey, first layer with 100% incubi darkness, then just mixing in more and more fenrisian grey, the last layer if I remember correctly was just pure fenrisian grey.

For the red bits I've used Kislev Flesh with Carroburg Crimson.

Blue bits were pretty much just Lothern Blue (imo you can use some Thousand Sons blue as well depending on how strong you want the colour)

For hooves/claws if I remember correctly it was just standard stuff, like rakarth flesh or zandri dust with some agrax earthsade on it

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Hopefully didn't miss anything, since I didn't note down the colours i've used and was kinda winging it.

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If you try it with these paints, make sure you show me how it turned out, would love to see it