No package in Mint20/Ubuntu20.04 (yet), needs to be build manually:

# make a folder to hold the tortoise source
mkdir ~/temp 2>/dev/null
cd ~/temp

# alias the python3 binary as python
sudo apt install python-is-python3
# now this should work, and return a 3.8.x version
python --version

# pip3 is needed to fulfill all the build dependencies
sudo apt install -y python3-pip build-essential

# install mercurial command line
sudo apt install -y mercurial
# pull tortoisehg source (stable branch)
hg clone https://foss.heptapod.net/mercurial/tortoisehg/thg -r stable
cd thg
pip3 install pyqt5
pip3 install qscintilla
sudo apt install -y pyqt5.qsci-dev
sudo apt-get install python3-pyqt5.qsci
pip3 install mercurial

# install one more necessary package
sudo apt install -y python3-iniparse

# build it
make local
# move it to ~/tortoisehg  (this is optional)
cd ~/temp
rm -rf ~/tortoisehg 2>/dev/null
mkdir ~/tortoisehg
mv thg/* ~/tortoisehg

Now you can create a dock/desktop entry:

vi ~/.local/share/applications/tortoisehg.desktop

and paste in these lines (replace “developer” with your username) :

[Desktop Entry]
Name=TortoiseHG
Exec=/home/developer/tortoisehg/thg
Comment=Launch TortoiseHG
Terminal=false
Type=Application
Icon=/home/developer/tortoisehg/icons/thg_logo.ico

Now you can hit the “Show Applications” button (the Start menu), search for Tortoise, and add it to favorites.