How to build a 12v 100+ Amp power supply (Transformer, Diode Bridge and Cap)?

Not in parallel.
If you segment the strips conveniently, and ensure the grounds are tied together, you can drive each 'string' of LEDs with a smaller power supply - e.g. 5 or 10A for the appropriate number of LEDs n each segment.

This will also simplify your cabling requirements - using a much smaller gauge of wire, and even if you did manage to push 12V@30A in one end of the string - the power buss would burn out about half way along the chain, as the tracks and interconnects are probably only good for 10A at the very maximum. (12 x 30 = 360Watts = heat)