Your first portrait is free, with no account. After that you have three options. Prices are shown in the app and in Google Play.
Four packs of 10 portraits is $9.99, a one-time purchase. You pick four themed packs of 10 portraits (40 in all) and can use them on up to 4 pets. They never expire.
Heartgild Pro is $99.99, a one-time purchase, with 600 portraits across every theme for unlimited pets. It is made for groomers, shelters, photographers and gift-makers. It also never expires.
Unlimited is $6.99 a week and renews weekly until you cancel in Google Play. Fair use applies: generation slows down after 100 portraits in a day and stops at 200 a day.