Rear derailleur needs a couple pedalstrokes to change gear
Only 500 km from new?  Sounds like cable stretch where the inner cable increases in length from new as it beds in.

Did you use up your free service?  Most new bikes from shops come with a 2-8 week "tweakup" to fix minor things like this.  If you bought the bike off the web, then its up you to fix it.

Firstly check out your brake line - there should be some form of barrel adjuster, often at the deraileur end.  Try undoing it a turn to tighten the cable (ie lengthen the outer), and see if it makes a difference to shifting.



Sometimes they're on the downtube (this is more of a road bike thing)



You shouldn't need to adjust anything else on your deraileur, so no screwdrivers or hex drivers needed.

This is easiest if your bike is hanging up off the ground so you can rotate the transmission.  Don't put your bike upside down, things don't work exactly the same the other way up.

Also its probably time to lube your chain.