Installing a debug-enabled Arduino core
Arduino cores are the key to making debugging available in the Arduino
IDE 2 for particular chips. If you want to install a new core, in most
cases, you first have to add a boards manager URL in the
Preferences dialog.
How to enter a new boards manager URL
First you need to open the Preferences dialog, which you find either in the Arduino IDE or the File menu.
Next you have to open the field Additional boards manager URLs and type in the package index URL, finishing with clicking on two OK buttons in succession.
Now type in the package index URL.
Once this has been done, you can search in the Boards Manager for the core, and install it.
How to install a new core
You need to activate the Boards Manager by clicking on the board symbol in the left side bar (1). After the boards manager pane has been opened, type part of the core's name into the search line (2). Then all cores with the search word in their description are displayed. Scroll down until you see the one you want to install (3). Install this core by clicking on Install (4).

ATTinyCore (Debug enabled)
This is a fork of Spence Konde's ATTinyCore version 1.5.2, which covers all classic ATtinys with a debugWire interface. With the advent of TinyCore (see below), it is deprecated. However, it might still be of interest to people who use the micronucleus boot loaders, which are not supported by TinyCore. You can install it after including the following URL:
https://felias-fogg.github.io/ATTinyCore/package_drazzy.com_ATTinyCore_index.json
TinyCore
This is a fork of Spence Konde's ATTinyCore version 2.0.0. It is the preferred way of supporting classic ATtinys. It does not support the micronucleus bootloaders, however. You can install it after including the following URL:
https://mcudude.github.io/TinyCore/package_MCUdude_TinyCore_index.json
MicroCore
This is a core for the ATtiny13(A). You can make it installable by adding the following URL to the Boards Manager URLs:
https://mcudude.github.io/MicroCore/package_MCUdude_MicroCore_index.json
MiniCore
This is the core for the small ATmegas with a debugWIRE interface, aka, ATmegaX8. You can make it installable by adding the following boards manager URL:
https://mcudude.github.io/MiniCore/package_MCUdude_MiniCore_index.json
XMiniCore
This is a debug-enabled Arduino core for the Microchip development boards ATmega328P Xplained Mini, ATmega168BP Xplained Mini, and ATmega328PB Xplained Mini. It is meant to be a replacement for the Atmel AVR Xplained-minis board package of the official Arduino distribution, which is already 10 years old and does not really work. The new core is a stripped-down and adapted version of MCUdude's MiniCore. The boards, together with PyAvrOCD, work very smoothly. It is just plug-and-play:
https://felias-fogg.github.io/XMiniCore/package_felias-fogg_XMiniCore_index.json
MightyCore
An Arduino core for ATmega8535, ATmega16, ATmega32, ATmega164, ATmega324, ATmega644, and ATmega1284, whereby ATmega8353 does not have a debugging interface. You can make it installable by adding the following boards manager URL:
https://mcudude.github.io/MightyCore/package_MCUdude_MightyCore_index.json
MegaCore
A core for most 64 and 100-pin AVRs. For example, the Arduino Mega (2560) is supported by this core. All of the listed MCUs are debuggable, but the ATmega128 has the problem that only hardware breakpoints are allowed. You can make the core installable by adding:
https://mcudude.github.io/MegaCore/package_MCUdude_MegaCore_index.json
MajorCore
This core covers just ATmega8515 and ATmega162, of which only the latter possesses a debugging interface. The additional board manager URL is:
https://mcudude.github.io/MajorCore/package_MCUdude_MajorCore_index.json
MegaCoreX
This is an experimental fork of the core for the megaAVR-0 chip family, such as the ATmega4809, which is used on the Nano Every Board and the Uno WiFi Rev 2. You can install the core (note: this is a work in progress!) using the following URL:
https://felias-fogg.github.io/MegaCoreX/package_MCUdude_MegaCoreX_index.json
The debug support for this core might not be bug-free (no pun intended). If you spot a bug, please report it.