I can vouch for Audin-Damian's Theorie de Morse et Homologie de Floer, read it cover to cover for my quals. They do Hamiltonian Floer theory with simplifying assumptions ($\omega$ and $c_1$ vanish on $\pi_2$ so there's no need to worry about bubbling, grading issues or caps, which one can learn from Dietmar's notes). They prove everything and provide intuition all along. The most technical estimates used for gluing are grouped into a Chapter that one can skip without loss of understanding. It also does Morse theory as a warm-up.