[hju hai hai fi]

Loss of liquids (derhoticisation/delateralisation).

[h] before a consonant devoices and fricativises the following consonant.
[çu hai hai fi]

Don't mind if I join a bit late.
Palatalization of consonants before front vowels:
[çu hai hai fʲi]
Seems likely enough to me.

Fortition of fricatives.

[cu hai hai pi]

I see your fortition and raise you pre-aspiration of unvoiced plosives!

[ʰcu hai hai ʰpʲi]

"Fortition of fricatives" seems to have excluded [h], but I'll go with it the way it is.
[ai] becomes [a:] like in some dialects of English (other diphthongs may be affected too):
[ʰcu ha: ha: ʰpʲi]

"Fricative" is really a misnomer for [h] since it isn't actually produced with audible friction. It's called a "voiceless glottal fricative" mostly for historical reasons, and because it does sometimes pattern with the fricatives of a language.

But it iskind of a boring consonant, so let's shift it to a pharyngeal approximant contiguous to low vowels:

[ʰcu ʕ̞a: ʕ̞a: ʰpʲi]

Good enough. After all, the latest version of the IPA chart does in fact have /h/ exactly between the fricative and approximant boxes.

I'm not certain [h] would shift simply on the basis of its being "boring", but I'll leave it alone.
Fronting of back vowels before palatals:
[ʰcy ʕ̞a: ʕ̞a: ʰpʲi]

You mean after palatals.

And how did linguoboy get [pʲi] from [pi]?

Anyway,

tonogenesis!!! Preaspiration becomes a high tone on the following vowel.

[cý ʕ̞a: ʕ̞a: pʲí]

Sorry, whoops.

He didn't. [pi] was a mistake -- it was supposed to be [pʲi].

Since this is a tonal language now, I'll play too. Long vowels become vowels with high tones:
[cý ʕ̞á ʕ̞á pʲí]