This question is about the same Krazy Kat strip (25 July 1936) as in Krazy language in Krazy Kat, 25 July 1936, in which Krazy is making a lot of classical references and Pupp is responding:
Krazy: Regular, the romin - insulting the kottage injins -
Pupp [to Ignatz, who's getting reading to hurl a brick]: Avaunt - wastrel
Krazy: Hoikillitz tossin the big bed bull -
Pupp: Have at you - Quince.
Krazy: Etlitz jugglin' a lot of woils -
Pupp: Kavvy Kannem -
Krazy: Horachel diffendin' his bridges -
Pupp: Shis kibab -
Krazy: Cyklops destroyin' the tutty-nine dumb dimmins
Krazy: Jupita darin' the tunda bolds -
Pupp: Sayonara -
Krazy: Ajex knoggin' the lightnin' around -
Pupp: Weeny weedy weeky
Krazy: Nobil - movillis - killosis -
Pupp: Hark - - I seem to hear the plaudits of my people.
As laid out in Spagirl's excellent answer, Krazy's remarks refer to, respectively: Regulus defeating the Carthaginians; the seventh labour of Heracles; Atlas holding the world; Horatio defending the bridge; a Cyclops fighting demons (?); Jupiter throwing thunderbolts; Ajax defying lightning; "noble - marvellous - colossus".
My question is: how do Pupp's remarks connect respectively with these? From Heracles to Quince, Atlas to cave canem, Horatio to shish kebab, etc. - what are the links?
(Spagirl's answer speculates a little about this in the final paragraph, but I'd like to see more detail, and I'd feel bad about asking her to go into full detail about this in her answer when it isn't technically part of that question. Hence, this new follow-up question.)