In order to boost the ouput voltage from 12 volt to 13.8 volt

You cut all wires coming out of the supply keeping only the various 12 volts wires which are soldered together and also 1 wire giving 5 volts .

locate the Pulse Width Modulator which drives the switching transistors .It is the brain of the supply ! Generally it is a small digital circuit (reference TL 494 or something else ending with 494 having 16 pins ) .

To increase the output voltage you only have to put a resistor between pin 1 and 7 .

The value has to be adjusted in order to get the 13.8 volts at the output .(the value is between 10 and 20 Kohms )¹⁾

It should be noted that for some power supply ,to have a good regulation of the output , it is necesary to load the 5 volt circuit with a resistor in order to have some current anywhere between 0.5 and 1 amp .