Here is that analysis without general relativity. It is attached.
That's only the explanation of the, I would say, the "initial forces", gravity and centrifugal forces.
This 'static' approach can only explain tides up to 0.8m.
After this come complicated effects like wave propagation, bathymetry - influences of the shape of the sea ground and the coast line - and resonance.
A short "uneducated" explanation, I put together for me. I'm not claiming that this is scientifically correct:
The tidal waves - yes, waves is the best model for it - are initially build as ultra long waves on big oceans. A low (0.5m) but very wide (thousands of square miles) bulge of water, following the attraction of the moon. It's a bit like a tsunami. As these waves approach the coast, these are "compressed" by the rising sea ground and in places additionally by the form of the coast (e.g. Bristol Channel). The waves are getting shorter, but to compensate for this, much higher.
In other places a tidal wave of one high water may be reflected on the coast or diverted, so that it overlaps with the next tidal wave, building a even higher tidal wave by resonance (Bay of Fundy, also North Sea).