It's a little confusing, but if you take it one step at a time it's not too bad.
You have two options:
1) Make sure your BIOS/UEFI is set to run virtualization. Google VMWare 6 and install it. Follow the directions mentioned, and you should be all set. However, once you're running Mavericks in VMWare you will need to install the original iLife disc or download (i.e., pay) the apps from the App Store. If you can find the disc, install iLife. After you have installed/purchased the apps, you can pause the downloads just after they start. There is no need to update to the new iLife apps in the VMWare, you only want the process to start.
Once that is all set, go back to your Hack and update your iLife apps normally. All should be well.
2) Boot with a Clover boot loader USB. I don't know anything at all about Clover, but this option is sort of like booting with UniBeast. You set up the USB with Clover as mentioned, and then you make sure to have your BIOS/UEFI boot with the USB instead of your HDD. After booting with the Clover USB, you go into your Mavericks install. You should be able to update normally.
After you update you can shut down your system, remove the USB, and then return to normal booting with the TonyMacx86 tools (i.e., Chimera). Clover will not be necessary after updating iLife.
Since you don't have the iLife discs anymore, it may make sense to go the Clover route. If you think that the VMWare is easier, and you're okay with paying for the apps again, then you can go that route.
Personally I wasn't sure which way to go, but I really didn't understand the Clover USB process so I went with VMWare. I found it to be pretty simple once I started. However, I still have my iLife disc.