I have the exact display and spent a few hours trying to get it to work with a 328p chip running at +5V.
The connections given above are correct with the exception of needing resistors for voltage shift and a divider on the SCL pin.
Without the 2k to ground to divide the 5V Arduino D13 driving the SCL pin, the display would ghost horribly. Only turning off the SPI pins or grounding the SCL would produce a stable display.
I also swapped the DC/Reset pins to match Adafruit graphicstest sample.
LED- --- GND
LED+ --- to +5V through a 120 ohm resistor, can increase resistance to dim the backlight
CS --- Arduino D10 (CS), through a 1k resistor
SCL --- Arduino D13 (SCK), through a 1k resistor and a 2k to ground (effectively forming a voltage divider for the signal).
SDA --- Arduino D11 (MOSI), through a 1k resistor
A0 --- Arduino D8 (DC), through a 1k resistor
Reset --- Arduino D9 , through a 1k resistor
VCC --- +5V, NOTE: that the display has a J1 on the back, open means 5V, closed 3.3V. Mine is open.
GND --- GND
This hookup works with the Adafruit ST7735 library sample graphicstest.
I also tried using the minimal program from http://w8bh.net/avr/AvrTFT.pdf, here is a gist with the code in text format, PDF tends to mess up the text order: https://gist.github.com/vsch/4c173dfc92772ac2d11de16fe1c2d94c
The gist pin definitions for DC/RST are swapped to match the Adafruit graphicstest ones so either can be burned without changes.