In order to unpack a ZIP file that's located on your phone, you can make use of the unzip command, which is included in BusyBox. To execute it, you can either install a Terminal emulator on the phone, or use adb from a computer with your phone plugged to it via USB.
ADB method
Before plugging your phone to the computer, make sure that the checkbox near USB debugging, located in the Developer settings, has been selected.
Next, plug your phone to the computer, start a shell on the latter and install ADB, which you'll use as a means to execute commands in your phone.
After the installation is complete, start ADB by issuing adb shell, which will trigger an authorization dialog on your phone's screen. Accept it, and focus on the newly issued command, since you might have noticed that a new, differently prefixed shell has taken your previous one's place on the computer: you're now commanding your phone.
Now, from the ADB shell, cd to the directory where your ZIP is located, and create a new directory with mkdir Directory (replace Directory with a name of your choice).
Finally, issue unzip archive.zip -d Directory, replacing archive.zip with your archive's name; the contents of the archive will then be extracted to the specified Directory.
Should you find too much output cluttering your shell, replace the unzip command above with unzip archive.zip -d Directory &> /dev/null, which will silence the command.
