It’s fairly easy to replace the slightly unfriendly syslinux with grub (grub2) in Alpine Linux. I use v3.6 but YMMV.

Notice how I use the tool blkid to find the Linux root device. The grub root device, however, needs to be the first partition, which is a bit confusing.

alpine:~# apk del syslinux
alpine:~# apk add grub grub-bios
alpine:~# grub-install /dev/sda
alpine:~# blkid 
/dev/sda3: UUID="caff7641-b9d3-435a-8282-fc3b15ae8b3a" TYPE="ext4"
/dev/sda2: UUID="fe051023-0986-425e-af4c-5e34a24d4756" TYPE="swap"
/dev/sda1: UUID="1c6b6010-4dff-4d10-881f-16899bd4c227" TYPE="ext4"
alpine:~# cat <<EOF >> /etc/grub.d/40_custom

menuentry "Alpine Linux" {
	set root=(hd0,1)
	linux /boot/vmlinuz root=UUID=caff7641-b9d3-435a-8282-fc3b15ae8b3a modules=sd-mod,usb-storage4,ext3 quiet
	initrd /boot/initramfs-vanilla

Or edit the file with mg /etc/grub.d/40_custom to add the above menuentry.

Now create the grub.cfg file from the templates in /etc/grub.d/*:

alpine:~# grub-mkconfig -o /boot/grub/grub.cfg