A number of Pokémon in Brilliant Diamond and Brilliant Pearl do not evolve through the simple level-up method. The psychic-type Pokémon Chingling, in particular, requires two additional conditions to be met. To evolve into Chimecho, you must both have a high level of friendship with your Chingling. Also, Chingling can only evolve at night.
In Pokémon Brilliant Diamond and Brilliant Pearl, “night” is whenever it's dark outside the game, which runs from 20:00 pm to 3:59 am with your Switch's time settings. In theory, you can go to your Switch's “Date and Time” settings, unsync it from the Internet, and manually change the game to be nightly. But who would, right?
However, the time of day is the easier half of Chingling's evolutionary conditions. You must also have a great friendship with your Chingling. Ways to strengthen your bond with your Pokémon include keeping it in your party, not letting it pass out, taking it out of its PokéBall for a walk, and feeding it Poffin and vitamins. You can tell if your friendship is high enough by checking if your Chingling shows two hearts in the Pokétch friendship check.
A note here from the author, though: my Chingling actually evolved before showing those two hearts on the Friendship Checker. However, my Chingling had been at my party for a long time without interruption, I had given him some vitamins and had been walking on it for a while. He wasn't as fussy as my Budew, which suggests that the Pokémon's personality type might also favor how easy it is to evolve.