my engine dies when i turn on all the electrical components in the car

at idle, test 9, battery voltage i think
indicates approximately 13.4-13.6

when i turn on the aircon, this drops to around
12.5 - 12.8

when headlights are on, this drops to 12.1 - 12.2

when i engage the gear, it goes down to
11.7 and then, it cuts out...

i placed a tester on the battery, the results indicate a
voltage of 13.5 and does not change,

what could possibly be wrong here?