Tiny Core Linux Install guide.

The follow steps will install a bootable tinycore on the VM's drive:

1. Click anywhere on the desktop
2. Select  [system tools] -> [App Browser]
3. Click the [Connect] button. 
4. Type cfdisk in the search box
5. Select cfdisk
6. Click [Go] button
7. Type grub in the search box
8. Select grub-0.97-splash.tcz
9. Click [Go] button
10. Open a terminal

sudo su
# to make a new partition.
cfdisk /dev/hda

11. Select [new] -> [Primary] -> [bootable] -> [write]

# to put a filesystem on the new partition
mkfs.ext3 /dev/hda1
rebuildfstab
mount /dev/hda1
mount /dev/hdc
mkdir -p /mnt/hda1/boot/grub
mkdir -p /mnt/hda1/tce
touch /mnt/hda1/tce/mydata.tgz
cp -p /usr/lib/grub/i386-pc/* /mnt/hda1/boot/grub/

# Edit menu.lst
vi /mnt/hda1/boot/grub/menu.lst

# Add following values in the menu.lst
  default 0
  timeout 5
  title tinycore
  kernel /boot/bzImage quiet
  initrd /boot/tinycore.gz

grub
  root (hd0,0)
  setup (hd0)
  quit

cp /mnt/hdc/boot/bzImage  /mnt/hda1/boot/
cp /mnt/hdc/boot/tinycore.gz /mnt/hda1/boot/
umount /mnt/hda

12. shutdown, and remove the tinycore iso from the VM's storage devices. Start the VM.

Reference