Here is the full list of all 43 Birthdays the Beginning trophies - there are 26 bronze, 13 silver, 3 gold and 1 platinum.
Exceeded 10 billion in total organisms.
Captured the ancient fish, Latimeria.
Captured an ammonite.
Captured the stench blossom, Rafflesia.
Achieved Cube temperature of 60°C.
Achieved Cube temperature below 0°C.
Obtained "Aquahexahedron" and made the entre Cube into land.
Made the entire Cube into sea.
Captured the elusive Nessie.
Captured a 9-star rarity organism.
Made the deepest sea on the largest Cube.
Made the highest mountain on the largest Cube.
Cleared 1 challenge.
Cleared Scenario 4.
Captured the giant panda, Ailuropoda melanoleuca.
Exceeded 1 billion total organisms.
Captured the olive tree, Olea.
Captured the domesticated dog, Canis familiaris.
Cleared Scenario 3.
Captured the ancient pachyderm, Mammuthus.
Captured the ancient bird-lizard, Archaeopteryx.
Captured the primitive dragonfly, Meganeura.
Captured the terrible lizard, Tyrannosaurus.
Captured the primordial plant, Prototaxites.
Captured an SS-sized organism.
Cleared Scenario 2.
Moved terrain over 10,000 times.
Captured the prehistoric fish, Coelacanthus.
Moved terrain over 1,000 times.
Cleared Scenario 1.
Captured your first organism.
Used an item for the first time.
Obtained all trophies.
Raised Avatar's level to max.
Captured every organisms.
Accumulated over 10 billion total Cube Years.
Accumulated over 100 billion total Cube Years.
Accumulated over 500 million total Cube Years in Free Play mode.
Captured the giant squid, Architeuthis.
Captured the Grand Watcher, Smilodon rex.
Cleared all challenges.
Cleared with a result of 4 stars.
Cleared with a result of 5 stars.