Engine overheating

Hi, my car (a toyota sedan ) has been having an overheating problem so I first thought it was caused by the lose radiator cap, which we replaced with a more fitting one.

Still especially when driving uphill or accelerating at high speeds, the engine overheats and you can hear a "boiling" sound coming from the radiator.

The coolant reservoir also tends to fill up during this (about after 40 kms of travel).

my mechanic tells me we have to replace the cylinder head gasket and do a refacing.

Do you think there could be any other problem which I may need to check first before doing this since it also doesn't sound cheap?