Danganronpa 2: Goodbye Despair Anniversary Edition

Raising a pet has 4 stages with varying steps and things to do (whenever you get enough steps to advance a stage, a little Monomi notification will appear at the bottom left):
The first stage is when it is just an Egg which takes just 100 steps to Hatch moving on to Chibimi.

For Chibimi you need to take 1000 steps to evolve into one of the 6 potential pets while also cleaning the poop your pet drops every 100 steps (because if you leave it then the pet's despair level will rise, once it reaches 10 your pet will die unless it's a monokuma), you can also give the pet gifts to raise its Hope level (the type of gift is irrelevant as every gift will raise the hope level by 1). This is the stage that you decide which pet you would like as well as the level of "Hope" and "Despair" determines what pet you will get when they emerge from the Cocoon.

For the third stage when your pet is in its Cocoon you just need to take another 100 steps for it to emerge as one of the six potential pets, (I am unsure if you can still give your pet presents during this stage as I gave my pet gifts before the Cocoon stage).

For the fourth and last stage you have another 1000-2000+ steps to take (depending on the pet you have), you will still need to clean up their poop every few hundred steps (unless its monokuma since it can't die, unless you want to clean anyway), once you've taken enough steps a notification will pop up at the bottom left and your pet will give you another egg before giving you some monocoins and some items (Usami and Monokuma will also give you a skill), they will then leave leaving you another egg which you can rinse and repeat this process for all the pets to get the "Gotta Raise 'Em All!" achivement.