RCBO independent circuit immediately trips, connected only to an air conditioner, what should I troubleshoot and what could be the problem?
Some possible bad news here. Air conditioning systems have a sealed compressor, the oil and Freon (or refrigerant) is in a sealed loop, one common failure mode is some moisture gets in the system and mixes with the oil, then the mix becomes acidic and etches the varnish off the motor windings, causing small ground faults at first and later full blown shorts inside the compressor.

I would verify it is not a wiring issue as jack and 3 phase suggest. If it is OK with the unit turned off or disconnected, this may be the issue.
A HVAC tech should have a megger (a high voltage ohm meter) that can verify if leakage from the motor windings to ground are the cause of the fault. 

A “window” type is usually not worth repairing, a small mini split may be worth repairing. I don’t know your laws but on this side of the pond repairs like this require a licensed HVAC person to recover the Freon and replace the compressor and filter dryer. Then the system is pumped down and flushed, the Freon, if not damaged, can be filtered and reused but, if it has turned black, it is replaced with fresh refrigerant and the oil charge verified. So you can see why we usually replace window units.