Oshawott is widely considered the best starter out of the other generation V Pokémon starters, so seeing it make a return as one in Pokémon Legends: Arceus was welcomed by many water-type fans. However, the starters you get in this game can never be shiny, but there are shinies in the game. Here is where you can catch a wild Oshawott.

Catching a wild Oshawott in Pokémon Legends: Arceus can only be done by completing the main story of the game and then traveling to the Alabaster Icelands and entering space-time distortions. In these distortions is where you can exclusively find shiny versions of Oshawott, Dewott, and Samurott, although the spawn rates for them are quite rare. Because of their low chances to appear, you may have to grind this out a bit, but you should get them eventually.

If you really do not care about finding shiny versions of these starter Pokémon, you can alternatively trade for an Oshawott or talk to Professor Laventon after completing the main story. He will give you the other two starters that you did not choose at the beginning of the game for free, so tirelessly searching the space-time distortions is not required to get all the starters.