How does outfit unlocking work?

It's a bit complicated, all in all it's a sort of a meta-game like unlocking The Lost in The Binding of Isaac Rebirth.

Each level has a special 5 digit code that unlocks an outfit. By finding the alien when replaying a level (they do not show up the first time) you can earn a chest. The chest will give either 50 coins, an outfit, or one of the 5 numbers of that level's outfit code.

You cannot find the codes yourself--your game will only ever show you one piece of the puzzle. Instead you're supposed to post the code to Miiverse, find the other 4 digits from other people, then enter the full 5 digit code on the Chibi PC. After this code is entered the Alien will have a 100% chance to give you the outfit if it's not already unlocked.

To cut to the point, you can simply find the outfit codes collected in this guide.

In a way it's cheating, but the real "game" was finding all the codes for the first time which is already done. If you look on Miiverse now you'll mostly just find those posts that compiled all the full codes anyway.

Giving all the Snacks to each Toy will also give you a costume based on that toy, entirely separate from the outfit code stuff. You can change outfits from any time at the pause menu.

Go to the Chibi-PC, choose Chibi-Outfit Network, and click on any world. There will be a list of levels of that world that have a costume. Enter the 5 digit code and it should tell you to go back, save the baby alien, and it will reward you with a costume. Remember, you must complete the levels first and then go back a second time to save the alien. To change the costumes, once you've earned them, you must go to the pause screen and it will have an option to change your costume. And when you save the alien, you dont have to worry about completing the level AGAIN. Just save the alien, get your costume, and just return to the Chibi-House. Your costumes will save. And as for the codes, dont worry, I got you. https://sirtaptap.com/2015/10/chibi-robo-zip-lash-outfit-code-guide/ All the codes for each level are here. Hope I helped!