For a more detailed guide with screenshots check out my guide on Steam: https://steamcommunity.com/sharedfiles/filedetails/?id=2120574329

Found the Blue Unicorn:

The blue unicorn is hidden behind a barrel in the northeast corner of the starting map - Starrest city - near to the text "Whispering Springs".

Found the Purple Unicorn:

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 behind the shack.

Found the Yellow Unicorn:

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. The yellow unicorn is hidden there behind the stone/wall.

So there are chests!:

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.