Successfully complete one of the following tasks to get a trophy:

Item Complete (Gold): Get all the items.
Mission & Big Game Trophy Complete (Gold): Complete all the missions and the big game trophy.
Complete Animal Encyclopedia (Gold): Complete the Animal Encyclopedia.

Additionally, there are 42 secret trophies:

Hippopotamus Yawn (Bronze): Complete Mission "The ultimate big mouth... You know who!".
Cheetah Hunt (Bronze): Complete Mission "Hunting at 60 mph".
Approach African Buffalo (Bronze): Complete Mission "Photo for "Nature Power" magazine".
Baby African Elephant (Bronze): Complete Mission "Looking for material for a new picture book".
African Elephant Showering (Bronze): Complete Mission "African Elephant cooling off in the water".
Wild Dog Hunt (Bronze): Complete Mission "The endangered African Wild Dog".
African Elephant Trumpet (Bronze): Complete Mission "Urgent! African Elephant"s powerful roar".
Leopard Hunt (Bronze): Complete Mission "A silent hunter that sneaks up on its prey".
Sunset and Reticulated Giraffe (Bronze): Complete Mission "A single shot that symbolizes Africa".
Mysterious Wall Painting (Bronze): Complete Mission "Investigate evidence of indigenous people".
Hippopotamus Fight (Bronze): Complete Mission "Victory hinges on the size of their mouths".
Gerenuk Eating Food (Bronze): Complete Mission "Urgent! Photo for "All About Mammals" guide".
Plains Zebra"s Intimidation (Bronze): Complete Mission "Wrath of the Plains Zebra".
Skull Collection 1 (Bronze): Complete Mission "Could you hunt down some animal bones?".
Lions Pride (Bronze): Complete Mission "Lion, king of the beasts".
Nile Crocodile Hunt (Bronze): Complete Mission "To my dear Nile Croc specialist!".
Pelican Cry (Bronze): Complete Mission "Urgent! Need that bird call".
Commemorative Photo with Masai (Bronze): Complete mission "Job: Piece to be included in photo book".
White Rhinoceros Family (Bronze): Complete Mission "Thanks! Our book is flying off the shelves".
Mysterious Footprints (Bronze): Complete Mission "Please go verify this rumor".
Collect Crittercam (Bronze): Complete Mission "Crittercam retrieval".
Travel side by side with troop (Bronze): Complete Mission "Urgent! Publicity still for our documentary".
Sunset and Oryx (Bronze): Complete Mission "The oryx and its long horns".
Baby Cheetah Cry (Bronze): Complete Mission "An adorable baby calling for its mama".
Skull Collection 2 (Bronze): Complete Mission "Clue to the mystery creature"s identity".
Lion Fight (Bronze): Complete Mission "Intergenerational battle".
Sunset and Cheetah (Bronze): Complete Mission "You"re a hit! Got time for another?".
Discover King Cheetah (Bronze): Complete Mission "King Cheetah with snake-like patterns".
Discover Pygmy Hippopotamus (Bronze): Complete Mission "The endangered Pygmy Hippopotamus".
Discover Black Leopard (Bronze): Complete Mission "Black Leopard lurking in the dark".
Discover Okapi (Bronze): Complete Mission "The rare and cautious okapi".
White Rhinoceros Fight (Bronze): Encounter "White Rhinoceros Fight".
Leopard vs Olive Baboon (Bronze): Encounter "Leopard vs Olive Baboon".
Cheetah vs Warthog (Bronze): Encounter "Cheetah vs Warthog".
Wildebeest River Crossing (Silver): Complete Mission "The wildebeest herd"s spectacular moment".
Masai Giraffe Necking (Silver): Complete Mission "Research Req: Fight between Masai Giraffes".
African Elephant Boss (Silver): Complete Mission "Mind risking your life for a photo?".
Lion Hunt (Silver): Complete Mission "Job: The king"s hunt".
Find Bottle (Silver): Find the bottle.
Cheetah on car (Silver): Encounter "Cheetah on car".
Complete Safari Mode (Gold): Complete Mission "The "Nunda", a giant beast of legend".
Jambo! AFRIKA! (Platinum): Completed AFRIKA! Congratulations!!!