You can unlock this achievement in any mode of play (single/co-op/Xbox live/local play) and on any difficulty. This is a main storyline achievement so it cannot be missed.
You will encounter Deathbird during the Shi'ar Empire mission.
She is pretty easy to defeat, when she is flying just use your ranged attacks/powers. When she swoops down to grab a hero you will be required to do several button presses to nail her to the ground. Once she is on the ground use close combat attacks/powers and switch back to long range when she is airborne again.
Repeat until she is halfway dead and get ready to destroy the crystal that heals her and makes her invincible to all attacks. It will activate in the middle of the room. Once destroyed continue your attack.
Once she is defeated the achievement is yours!