How to get hair from Tangerine Orange to Sky Blue?

I have done this and the other way round a few times, but I will warn you, never without damage. I have short hair so the damage never mattered to me but if your hair is long you may have to come to terms with losing some length.

Edit: sorry got the colours the wrong way round, so ignored the part about oranges covering blue haha
also since your hair is permanently dyed then colour remover is definitely
the best way to go. I assumed your hair was dyed with semi dyes.  You can use  them up to three times before they've stopped working and your hair should be a warm brown/blonde colour underneath. Colour removers are made for permanent dyes so you should have good resultslifting some of the Orange pigment with them.

After you have got the permanent pigment out then do bleach baths over coconut oil to lighten your hair. You should wait two weeks between bleach baths to give your hair time to recover. Never bleach to white. If you get your hair to the inside of banana colour you can tone it to white using a purple semi dye mixed with conditioner. Also since you have already done a bleach bath I would make sure to have some deep conditioner on hand, as colour removers are really drying so your hair will need some love before bleach bathing again.

You don't necessarily need white for all blue shades. You may find that you have staining that will prevent your hair from getting as light as you want. But a darker blue will cover stained hair better. I covered stained yellow hair with Sfx blue velvet with good results.

Thanks for your detailed response, Marthakins! So it's do-able. Great news! I look after my hair really well but I'm always concerned about going through the bleaching process as my hair is down to my waist.

I was hoping to go a pale sky blue, like a pastel shade. So would I need to go more of a white shade or would a purple semi do the trick too?

For a pastel blue you will need a very pale base, if you have some yellow left this will make the blue more of a turquoise shade, so if you don't want that you will need to tone to white first with violet.

So I've never toned before, would this be a form of processing or do you mean also using a purple semi? What products would you recommend either way?

Purple semi heavily diluted in conditioner, or violet shampoo/conditioner such as Touch of Silver, Bonacure etc left on for longer than recommended. This will remove any residual yellow tones from light blonde hair without any damage, but you need to bleach to the inside of a banana colour first.