There are three Lost Memories in Aquaria. Collecting all three memories will unlock a secret ending.
The first Lost Memory is in Mithalas, just before entering the Mithalas Cathedral. Look in a house along the left wall just west of the cathedral entrance.
The second is at the very top of the Sun Temple. In the map area before the boss room, follow the unkillable moving robots to a room with a gear. Spin to raise the water level and take the northwest hallway all the way up until the water ends, then wall jump to the top. Jump from one gear to another to reach the other side, then either using the Nature Form plant jump, or the Beast Form jump, bounce between the two lower center cogs, and up the other cogs until you reach a floating water ball by a northeastern hall exit. Take this up and wall jump the testube outside of the Sun Temple to the top and collect the second lost memory.
The last one is in the eastern section of the Abyss. Travel to the whale and sing him a song to enter his mouth (the song is water drop, swirl, circle, swirl, leaf). Once inside the whale, head to the back and an octopus will sing to you. Carefully listen to his song and then head back out to the main area inside the whale. Use the Sun Form to light up the four lamps. The order is east, north-west, south-west, center. Once you’ve successfully completed the puzzle go back to the octopus room and use the Bind song to pick up the pearl. Carry the pearl out of the whale, past the geysers, and into the central alcove in the map area. Place the pearl in the pearl slot, charge it, and enter for the memory. Don't forget to grab the Health Egg while you're inside the whale.