Code:

#define KEYCODE_NUM 6
typedef struct {
    uint8_t modifier;
    uint8_t reserved;
    uint8_t keycode[KEYCODE_NUM];
} keyboard_report_t;

static keyboard_report_t keyboard_report; // sent to PC

#define KEY_A                      4
#define KEY_B                      5
#define KEY_C                      6
#define KEY_D                      7
#define KEY_E                      8
#define KEY_F                      9
#define KEY_G                   10
#define KEY_H                   11
// [...]

#define NUMBER_OF_BUTTONS 8
// data type to use for storing the shift register data - make sure the datatype has >= bits than NUMBER_OF_BUTTONS
#define KEYS_DATATYPE uint8_t

uchar buttonCodes[NUMBER_OF_BUTTONS] = {KEY_A, KEY_B, KEY_C, KEY_D, KEY_E, KEY_F, KEY_G, KEY_H};

#define STATE_WAIT 0
#define STATE_SEND_KEY 1
#define STATE_RELEASE_KEY 2
uchar state       = STATE_WAIT;

// this reads the shift registers and fills the report buffer for USB directly to save some bytes
void readShiftRegisters() {
    uchar i;
    uchar offset = 0;
   
    // Trigger a parallel load to latch the state of the data lines
    PORT_SHIFTREG &= ~(1 << PIN_SHLD);
    // the SN74HCT165N is fast enough so we don't need a delay, this saves a few bytes
    //_delay_us(PULSE_WIDTH_USEC);
    PORT_SHIFTREG |= (1 << PIN_SHLD);

    // Loop to read each bit value from the serial out line of the shift register
    // we forge the keyboard report directly, to safe some memory
    for (i = 0; i < NUMBER_OF_BUTTONS; i++) {
        if (PORT_IN_SHIFTREG & (1 << PIN_QH) && offset < KEYCODE_NUM) {
            state       = STATE_SEND_KEY;
            keyboard_report.keycode[offset] = buttonCodes[i];
            offset++;
        }

        // Pulse the clock (rising edge shifts the next bit).
        PORT_SHIFTREG |= (1 << PIN_CLK);
        // the SN74HCT165N is fast enough so we don't need a delay, this saves a few bytes
        //_delay_us(PULSE_WIDTH_USEC);
        PORT_SHIFTREG &= ~(1 << PIN_CLK);
    }
}

int main() {
    // ...
    while (1) {
        wdt_reset(); // keep the watchdog happy
        usbPoll();
      
        // clear the USB report
        for (i = 0; i<sizeof (keyboard_report); i++) {
            ((uchar *) & keyboard_report)[i] = 0;
        }     
        keyboard_report.modifier = 0;

        // this fills the keyboard register directly
        readShiftRegisters();
   
        // characters are sent when messageState == STATE_SEND
        if (usbInterruptIsReady() && state != STATE_WAIT) {
            // we need this simple state-machine to send a single empty report (for "keyUp") when all buttons are unpressed
            switch (state) {
                case STATE_SEND_KEY:
                    state = STATE_RELEASE_KEY;
                    break;
                case STATE_RELEASE_KEY:
                default:
                    state = STATE_WAIT;
            }

            usbSetInterrupt((void *) &keyboard_report, sizeof (keyboard_report));
        }
    }

    return 0;
}