Pulse of Life is obtained by using Planet Protector five times. Aeris can equip the Cover Materia to speed up this process and use a Hyper to get Fury status. For specific grinding, the large forest in the Nibel Area past Mt. Nibel features many enemies (in large groups, helping other party members acquire Limit levels that require multiple enemy kills) with attacks that can raise Aeris's Limit gauge considerably due to their damage. One enemy fought here, Valron, uses Gravity-based attacks that reliably increases Aeris's gauge quickly with no risk of killing her.
Pulse of Life fully heals all party members, restoring their HP and MP to max, and curing them of all negative statuses. This provides great endurance for the party, reducing their reliance on Tents and healing items in longer dungeons. It also makes Aeris a great choice to heal the party in dire situations.
Between Pulse of Life and Planet Protector, Pulse of Life is better at rescuing the party in dire situations, while Planet Protector has utility elsewhere. Planet Protector instead allows the party to withstand strong incoming attacks from bosses, or to focus on being aggressive without worrying about healing.
Both Pulse of Life and Planet Protector are made redundant by Great Gospel, Aeris's ultimate Limit Break, which combines the effects of both.