To expand on juanpa.arrivillaga’s comment:
If you want to update Spyder in the root environment, then conda update spyder
works for me.
If you want to update Spyder for a virtual environment you have created (e.g., for a different version of Python), then conda update -n $ENV_NAME spyder where $ENV_NAME is your environment name.
EDIT: In case conda update spyder isn’t working, this post indicates you might need to run conda update anaconda before updating spyder. Also note that you can specify an exact spyder version if you want.