Via FTP tool: Just replace the radykal-fancy-gallery folder.
Via WP admin: Deactivate the plugin and delete it. Then upload the new zip and activate the plugin again.
In both cases you will not loose any of your created galleries and options.
All gallery options will be reset to default, so you have to reset them with your options.
You also need to reset all of your shortcode, because of the database changes!
Because you can set own options for each gallery, you need to reset the options for your galleries. Otherwise the defaul options will be used.
To run the upgrade successfully, you need version 1.2 installed. If you do not have it, you have to deactivate the plugin and install it again, this means also you have to set up your galleries from beginning.
This update needs a complete new installtion, that means all of your galleries will be deleted. Deactivate the plugin, replace the whole radykal-fancy-gallery directory in your plugins directory and activate it again.