There are two documents here.
The first are notes on a close reading of the text.
The second are notes on the two self-presentations of Socrates in the Apology, as Achilles and as a gadfly. My suggestions is that we can organize a number of features of Socrates’s self-presentation in terms of these two different models.
This chart summarizes two levels of meaning in Socrates’ self-presentation, one in which he compares himself to Achilles and the other in which he compares himself to a gadfly. The former is his self-presentation to most of the Athenians; the latter is his self-presentation to his fellow philosophers or students of philosophy. The former is fairly close to the canonical interpretation of the Apology which takes Socrates’ self-presentation unironically. The latter is the interpretation of Socrates’ speech if one assumes that most of it is meant ironically. A full interpretation of Socrate’s irony must take into account both self-presentations, understand who each one is meant for, and why Socrates presents his mission and purpose in two different ways.