How to set-up a shelf in a tiled bathroom?
You have some nice tile there. It would be a shame to drill holes in it. 

If you look at the customer reviews on the IKEA product page you can see this. You might want to consider that.



Review Source

If you do decide to use 3M Outdoor Mounting Tape some things to consider:


This tape is considered a permanent mounting system. 
Make sure that both rails of the assembled shelf fit nice and flat against the walls on both sides of the corner where you intend to mount the unit. 
You will want to make sure that the walls and rails are clean and free of any soap or oil film. I recommend a final cleaning with alcohol.
Attach the tape to the rails after you have fully assembled the shelf frame.
Attach the tape to the rails full length. If two runs fit the width of the rail then cover the full rail width.
Push the shelf unit into the corner carefully so that the two rails come into contact with the walls at the same time.


I have used this tape in the past and it adheres like crazy. Using it to mount metal rails really does mean that it will be there for the duration. 

The tape seems to me to offer an advantage over the recommended two screws at just the top. It will hold the shelf securely in the corner without the bottom end being able to pull out from the corner.