What cancels first?

HLC. Bossk can't do his thing until you've been confirmed to hit, which means all the way into Compare Results. HLC downgrades (not cancels) right after the initial roll.

Important thing to note is that crits acquired after the initial roll, whether from rerolls or adding/changing dice (such as Mercenary Copilot), are not downgraded by HLC. It triggers once immediately after the initial roll only, so while it definitely works at cross purposes with Bossk, it doesn't completely invalidate his ability.

Okay, time to get specific:

Quote

1. Roll attack dice

[Heavy Laser Cannon modifies crit results here]

1a. Defender modifies attack dice

1b. Attacker modifies attack dice

2. Roll defence dice

2a. Attacker modifies defence dice

2b Defender modifies defence dice

3. Compare attack and defence dice

3a. Each evade cancels one attack dice, hits before crits.

3b. If at least one hit or crit result remains, the attack is declared a hit.

[Bossk's effect happens here]

3c. Resolve all hits first, dealing one damage each time, then resolve all crits.

4. Mock your opponent's ancestry.

Does that make the timing nice and clear?

You forgot Step 5:

Hear the lamentation of the women.