If a player's "on attack" trigger kills an enemy unit at a battlefield with deathknell, does the deathknell effect happen before you move into the main part of a showdown?

Yes — the Deathknell resolves during the Combat Showdown Step, before combat damage is dealt.

Here's why: An "on attack" trigger fires during Step 1 of Combat (the Combat Showdown Step, Rule 459). When that trigger resolves and kills a unit with Deathknell, the Deathknell trigger becomes a Pending Item on the chain (Rule 428.1.a.1.b). Since the chain is still active within the Showdown Step, the Deathknell must go through normal FEPR — Finalize, get placed on the chain, and resolve — before the Showdown can close.

The Showdown cannot close while chain items exist (Rule 348). Only after the chain empties and all players pass does the Showdown close, and only then do you proceed to the Combat Damage Step (Rule 348.1).

This is distinct from Deathknell caused by combat damage itself — that Deathknell happens during Combat Cleanup (after damage), in a separate sequence. But a Deathknell triggered by an "on attack" kill resolves right then and there during the Showdown Step, well before anyone assigns combat damage.

Bottom line: The Deathknell resolves fully during the Combat Showdown Step. The unit is dead and its effect happens before combat damage is even calculated.