What are the most challenging taxi manoeuvres that a typical commercial airline pilot must execute?
"Most challenging" is a matter of opinion, but if I were to pick, it is probably the 180 degree turn.

The purpose of the maneuver is to turn the aircraft around and face the opposite direction. The technique is to position the aircraft to one side of the runway (taxiways are generally too narrow for this), then apply maximum steering angle, minimum thrust as well as differential braking (i.e. braking on the inner set of wheels only).

The challenge is that the nose wheel, outer set of wheels, outer wingtip and the tail each have their own turning radius. It is made even trickier when the nose wheel is a good 20~30 feet behind the cockpit. The pilots will be above the runway grass while the nose wheel is still on the pavement.

This maneuver is challenging enough that most aircraft manuals I've seen (e.g. B737, B777, A320) dedicate a good 10~20 pages just for this. Here is an example diagram for the B737-600:


B737 FCOM Volume 2, Section 1.10.7

This maneuver is mostly executed on small airports where there is no taxiway connecting to the end of the runway. For example, the only taxiway connection to the runway might be at the runway's middle length. A plane that wishes to use the full runway length to takeoff will have to turn onto the runway, taxi down half its length to the end, then execute a 180. On large airports this is rarely an issue, although a 180 might be useful when part of the taxiway / runway is blocked due to an incident.