Planet Protector is obtained by Aeris killing 80 enemies after she has unlocked Breath of the Earth. A good place to do this quickly is the large forest in the Nibel Area past Mt. Nibel, where six enemies can be fought in a single wave (Battery Caps), and approximately 4.4 enemies appear per encounter. Aeris can equip Magic Materia with All, or use Enemy Skill Materia abilities such as Aqualung, to kill multiple enemies quickly, taking advantage of her very high Magic stat.
Planet Protector grants temporary invincibility to party members. This can either provide an opportunity to heal other party members while they are safe from damage, or to focus on being aggressive and dealing damage with no fear of damage. Aeris can also save the Limit Break for a boss's more powerful attack.
Using Planet Protector five times grants Aeris her second level 3 Limit Break, Pulse of Life. This fully heals party members' HP, MP, and cures them of all negative status effects. Pulse of Life is a better choice if the party is particularly low, or if they are afflicted with negative effects, while Planet Protector is good if the party is not low or to protect against a boss's particularly powerful effect.
Great Gospel, Aeris's ultimate Limit Break, outclasses both Planet Protector and Pulse of Life, meaning it should be equipped instead once obtained.