This page describes how to add the AVR Dragon as programmer to the Arduino IDE, compile for ATTINY13 and program as such the ATTINY13 directly from within the Arduino IDE.

As described here, copy paste the following url

https://mcudude.github.io/MicroCore/package_MCUdude_MicroCore_index.json

Into Arduino IDE at: File → Preferences → Additional Boards Manager URLs:

Then click on OK.

Then select the newly added Board via: Tools → Board → Boards Manager…

Search for MicroCore and click on Install.

Now a new entry will be listed at: Tools → Board → MicroCore → ATtiny13

Select this controller.

To make it possible to program directly with the AVR Dragon from within the Arduino IDE the ATtiny13, search for the following file:

$HOME/.arduino15/packages/MicroCore/hardware/avr/1.0.6/programmers.txt

And add the following lines at the bottom:

dragonisp.name=Dragon ISP
dragonisp.communication=usb
dragonisp.protocol=dragon_isp
dragonisp.program.protocol=dragon_isp
dragonisp.program.tool=avrdude
dragonisp.program.extra_params= -p attiny13 -c dragon_isp -P usb

Now the AVR Dragon can be selected via: Tools → Programmer → Dragon ISP

Follow the link to the connection diagram at the official github page getting-started-with-microcore will show how to connect the ATtiny13 to the AVR Dragon.

Then add following blink code:

void setup() {
 // initialize pin 4 (ATtiny leg 3) as an output.
 pinMode(4, OUTPUT);
}
void loop() {
 digitalWrite(4, HIGH);   // turn the LED on (HIGH is the voltage level)
 delay(1000);             // wait for a second
 digitalWrite(4, LOW);    // turn the LED off by making the voltage LOW
 delay(1000);             // wait for a second
} 

And compile, program and observe that pin 3 alternates between 0v and 5v in a 1s interval