It is very easy to remove old kernel entries from a debian based systems using apt-get purge linux-image-x.x.x.x but in arch linux we need to manually delete kernel images from the /boot folder (we can’t use pacman for removing old kernel images).
To delete lts-kernel or Kernel entries from arch linux grub boot loader.
delete the kernel image and related files you want to remove (the version you want to remove)
sudo rm -f /boot/vmlinuz-kernel_3.xxx
sudo rm -f /boot/initrd.img-kernel_3.xxx
Also remove any related modules
sudo rm -rf /lib/modules/kernel_3.xxx
Pro tip: If you have multiple kernels installed, say linux and linux-lts, by default grub-mkconfig groups them in a submenu. If you do not like this behaviour you can go back to one single menu by adding the following line to /etc/default/grub:
To rebuild grub menu run the following command.
grub-mkconfig -o /boot/grub/grub.cfg
Now reboot your system to see the changes in grub menu.