The most important things to do are: 1) know how to defend yourself; and 2) know when to attack.

Here are the ways to guard Nancy's and Azazel's attacks:

NANCY:
Machine Gun Moves - Crouching Guard or Lying Down (after getting hit)
(The other moves Nancy uses can only be dodged using sidestep.)

How to defeat NANCY: Memorize a character's 10-hit combo with timing and precision.
(NANCY is not affected by aerial combos.)

AZAZEL:
Tail Moves and the Laser Beam - Crouching Guard
Growing Arms from Below - Sidestep or Standing Guard (damages a little)
(The other moves Azazel uses can only be dodged using sidestep.)

Be careful of Azazel's Rollout, it can guard Azazel at the same time deal damage to you.

How to defeat AZAZEL: Memorize a character's 10-hit combo and/or aerial combo with timing and precision.

Both AZAZEL and NANCY aren't affected by throw attacks.

Have fun pressing those directional buttons and X, O, Triangle and Square.