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