Here's how to unlock the different endings!
When on the black omen, you will come across a Blubber Hulk (which at first looks like a tornado on the ground). Approach it and have Ayla use Charm which gives you the strength capsule. Run away and go back through the door you came through (with the two Nus) and repeat.
The Lost Sanctum is one of the new bonus dungeons added to the DS. In order to unlock this, you must unlock the Black Omen in 12,000 B.C. The Lost Sanctum will apear in 65 Million BC, and 600 AD in certain locations.
Once reaching the Arena of Ages, send your monster out to train until it returns back with an item. Once it returns, you will see the monster's status window showing the item it brought back. Without closing this window, press the A button to select the option "Train Monster" then press A button a second time and you will now be on the Consumables item screen. Press the B button once to return back to the original screen. This will duplicate the item that the monster brought back (though you will not see any evidence of this until you look in your own inventory). You can continue to do this to get 99 of that item. This is a great way to stock up on magic, speed, or strength capsules.
This new dungeon has three parts to it and can only be unlocked when you've completed the game by defeating Lavos.
Go to Guardia Forest in 600 AD. Once inside, take the first right and go to the upper path. While in the small clearing, you'll notice a bush in the upper left. Go next to the bush and it will begin to shake. Press A and a monster will pop out, leaving a Shelter as he runs away. Get the Shelter, and then leave the forest and reenter. Do this until you have as many shelters as you want.