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