Atmel ICE SAM connector pinout does not reflect the real pinout
So, for some reason, the pinout are totally messed up because they are 2 different connections.
The standard ICE cable holds 2 different connector, where one has less pin and a larger pin pitch (standard 100 mil but only 6 pin), while the other has all the pins but the pin pitch is very small (50 mil and 10 pin), but the connector on the ICE is 10 pin 100 mil, so you need an adapter.

I ended up solving the issue, making a self-made adapter for a 10 pin connector on standard 100 mil pitch, buying the flat cable and connectors, and using a breakout board that has the 10 pin connector ready for usage.
The next step was to map the pins, and that came easy since the ICE guide has the pinout of the SAM port using SWD mapping:

SWDCLK    4
SWDIO     2
Reset     10
VTG       1
GND       3


These are all the pin needed; once connected the flat cable to the breakout board, I did connect these wires and I was able to write on the chip without problems. The voltage was correct, and the chip was correctly recognized in Atmel Studio.

I just wish someone would tell me what pin set to use, what port and suggest me to ditch the original cable that came with the ICE from the start; but hope that this will help others like me, that just started with microcontrollers