Likely the best bet for Android 4. It lets you run a chroot-based Linux distribution (like Debian Wheezy) alongside Android.
If you manage to bypass the bootstrap, here is the performance you can expect on Android 4.4 (typically 1–2GB RAM, 32-bit ARMv7 CPU). termux android 4
While official support for Termux began with Android 5.0 (Lollipop), users with older Android 4.x (KitKat/Jelly Bean) devices still have options for terminal emulation and basic Linux functionality. Likely the best bet for Android 4