When looking to the sensor at the top (the black plastic with tube connector). You see that one corner of the black plastic is flat. That is pin 1. Down that row is pin 2 and 3. Pin 4 is opposite pin 3 and so on.
That is a 3.3V sensor with I2C interface. Is your Arduino Pro Mini a 5V or 3.3V board ?
Connect GND to GND. The Vcc is for 3.3V, connect SDA to SDA and connect SCL to SCL. Use 4k7 pullup resistors from SCL to 3.3V and from SDA to 3.3V.
I don't know if the SS/INT needs to be connected, I didn't read every document.
Everything at 3.3V is good. You still need those pullup resistors, but for testing it might work without the resistors (with a little luck).
Connecting INT to D2 is okay. D2 is an interrupt input.
It is hard to see to what the wires are connected.
Pin 1, orange wire to GND, okay.
Pin 2, yellow wire to VCC, okay.
Pin 3, yellow wire to D2, I can't see it, it seems okay.
Pin 5, gray wire to red wire to SDA (A4), okay.
Pin 6, purple wire to red wire to SCL (A5), okay.
So yes, as far as I can tell, that is okay.
Run the i2c_scanner : Arduino Playground - I2cScanner
If the sensor is detected, the I2C bus is working. After that try to find a library for the sensor.