TerminalIDE is fantastic. comes with bash, ssh, tmux, vim, and git. And you can install other things as well.

I had no problem pulling in my github dotfiles repo and having everything set up just the way I want.

I don’t use tmux except when I connect the phone to a full size monitor. Then I also have a usb keyboard attached, and it’s like a full linux experience.

Does not require root.

https://play.google.com/store/apps/details?id=com.spartacusrex.spartacuside&hl=en