Let us remember that irony is used to describe something which is actually the opposite of what it pretends to be. If we examine the titles of these three chapters and then the action which is contained therein, we can see how this irony operates.
Firstly, in Chapter 12, entitled "The Fellow of Delicacy," we are presented with Stryver and his intention of proposing to Lucie Manette. However, it is clear from the way he talks of Lucie that he is definitely not a fellow of delicacy, and is indeed an arrogant, selfish individual. Note how he cannot believe that Lucie would ever refuse him, and how he refers to her after Mr. Lorry has told her not to propose:
Having supposed that there was sense where there is no sense, and a laudable ambition where this is not a laudable ambition, I am well out of the mistake, and no harm is done. Young women have committed similar follies often before, and have repented them in poverty and obscurity often before.
He is anything but a man of delicacy through such words. By contrast, Chapter 13, entitled "The Fellow of No Delicacy," presents us with Carton's proposal to Miss Lucie Manette, where he is shown to be a man of great care, love and consideration. Sydney Carton is brutally realistic about his chances, and even expresses gladness that he knows he will not be successful:
I know very well that you can have no tenderness for me; I ask for none; I am even thankful that it cannot be.
He, unlike Stryver, holds Lucie's happiness over his own, thus showing he is a fellow of considerable delicacy.
Finally, Chapter 14, "The Honest Tradesman," lets us observe the life of Jerry Cruncher and how he oppresses his wife and how his very dishonest trade of gravedigging is such a part of his life. Gravedigging was illegal at the time, and so there is considerable irony in presenting Jerry Cruncher as an "honest" tradesman.