Two things, if you take off the drive-side (R) of the crank and the 'axis' moves while you hold onto the chainrings, then the crankset needs replacing (or at the very least, this drive-side part).
Secondly, if there is too much play in the 'axis' while it is still in the bottom bracket, then the bottom bracket cups are probably worn out and will need replacing. I've heard it is possible so service these cups by taking off the plastic rings, but never tried it myself. The cups are usually inexpensive.
Square taper bottom brackets usually last longer but are heavier.
I'm assuming these are already attached to your frame, so you'll need a tool like this too:
