NQP implements a subset of Perl 6 that is useful for writing a compiler, and that runs well on parrot without the need for built-in functions (except the regex engine).

How exactly is this entire bootstrapping done?

Since NQP transforms its input to a format called PAST, the first step will probably be to write a PAST compiler that emit JS. Since the PAST compiler is now written in PIR, the bootstrapping plan might look like this:

1. Re-write the PAST compiler in NQP
2. Add a variant of the PAST compiler that emits JS
3. Run the NQP-on-parrot on itself, emitting javascript
4. reiterate until it works
5. Profit!