In each level, you will find pets to rescue. Give them items in the pet menu and try to match their characteristics. When they are ready to adopt, in the adoption menu pair them with a human once again matching characteristics. Slowly a bar will fill and give you skill points (a total 4). After the story missions side missions will pop to help you fill the bar.
14 more skill points when finishing missions.
In the upgrade menu upgrade stamina.
Full achievements guide:
00:29 LexBot Lover, Safe and Sound Achievements
04:05 Super Duper Dog Achievement
04:28 Talk about Pets
05:58 Talk about Adoption + Happy Home Achievement
06:33 4 Skill Points from Adoption
07:00 14 Skill Points from Missions
07:12 Max Health, Max Stamina, Lanterns Light, Canine Conduit, and Goddess of Olympus Achievements
08:39 If you don’t have enough Skill Points
09:08 Slithery Situations and Guardian I Achievements
10:01 Tangled Trouble and Guardian II Achievement
10:56 Luthor Lock Up Achievement and Guardian III Achievements