As you can see in the screenshot below the blue unicorn is hidden behind a barrel in the northeast corner of the starting map - Starcrest city.

As you can see in the screenshot below the purple unicorn is hidden behind a shack in the map JYHM Waters. To get there run east in JYHM Waters until you hit the edge of the map and then go south. You need to cross two bridges and then you will find the unicorn on the little island.

In order to get to the yellow unicorn you need to go to level two of the Frostbreath Ice Fields (southwest in level one). Once you are in the map you have to go to the southwest corner of the map. As you can see in the screenshot below the yellow unicorn is hidden there behind the stone/wall

CARE: The chest won't be there if you already have 999 achievements and you will have to start a new game for this achievement

The lost chest is located in the map JYHM Waters. In order to get there you need to run south until you hit the third bridge. Once you are there you have to dash onto the water and keep on dashing/walking until you hit the west edge of the map. Once you are on the west edge of the map you will see the chest as you can see in the screenshot below.