STORY OF SEASONS: Friends of Mineral Town

This achievement is pretty tedious if you start it late because it can take about 3 years to get it. Why and what you have to do to get pets is listed below.

How to be able to get pets in SoS:FoMT
If you already played Harvest Moon Back to Nature on PSOne or Friends of Mineraltown on the GBA you may think that you get your first pet from the beginning like in stardew valley. However, in the "Remake Version" you have to prepare more then a whole season for preparing the pet shop from Van. For him to appear you have to make the Harvest Goddess 30 presents (1 per day [I would advice doing this anyway from the beginning for the achievement where you have to make her 300 gifts. As a side note, this is missable because You can find her at the waterfall above the Hot Spring. Just throw presents in it and she will appear. It doesn't matter if she likes it or not.

When and where to find Van
Now that you unlocked Van and he introduced himself to you on the first sunny Wednesday after the 30th present to the goddess, you can buy pets from him once per season on the Rose Plaza on the 15th with sunny weather. If there is rain, snow or a storm (obviously) he won't be there. So another advice: save your data on the 13th before you go to sleep. Check the weather in the morning for the 15th and if it isn't sunny, reload and do it again. He will be there from 12 AM to 6 PM.

Buying pets from Van
Now you can buy some pets. But it's not as easy as you think, buying 5 pets instantaneously. A pet costs from 10.000G to 30.000G. Furthermore, to get the next pet, you have to raise the heart level of your pet to 8 by talking to it and giving Pet Treats. You can buy these from Van for 1.000G, too. But don't worry, you don't need 8 hearts on every new pet. You just need a total of 8, 16, 24 and 32 hearts on these pets (the horse doesn't count). So if you don't stop raising the heart level until 10 on your first pet you just need 6 hearts on the second one and so on, making it easier with every new pet. If a pet is getting the needed heart on the 15th itself, like getting the 8th heart on your first pet on the 15th, you won't be able to buy the next pet. It has to raise at least on the 14th. So you will never be able to buy two or more pets on the same day. 5 pets are the limit, so you can't buy all 8 pets that are available.

If you are interested, for me it took a whole season to get 2 hearts for my pet talking to him and giving him treats every day.

Last but not least, here is a list of what pets you can buy in which season and how much it costs.

Spring (Cats)
American Shorthair (20.000G)
Bengal (20.000G)
Calico (20.000G)

Summer (Penguins)
Penguin (30.000G)
Navy Penguin (30.000G)

Fall (Dogs)
Mineral Dog (10.000G)
Black Shiba (20.000G)
Papillon (20.000G)

Winter (Capybara)
Capybara (30.000G)
White Capybara (30.000G)