Hackintosh for Gigabyte GA-Z77-DS3H rev1.1 motherboard using OS X 10.8.5 Mountain Lion.
This is a minimal guide that fits my hardware configuration.

Intel Z77 chipset.
Supports 3rd Gen. Intel 22nm CPUs and 2nd Gen. Intel Core CPUs (LGA1155 socket).

Onboard devices:

• Qualcomm Atheros AR8161 Gigabit Ethernet controller
• Realtek ALC887 audio chipset

Sources:

• AR8161 LAN on new MoBo revisions (ga-z77-ds3h and ga-h77-ds3h, others)

Latest BIOS: version F9 (2012/09/27 update)

• Save & Exit / Load Optimized Defaults
• Peripherals / SATA Mode Selection - AHCI
• BIOS Features / Intel Virtualization Technology - Disabled (or add kernel flag dart=0)
• BIOS Features / VT-d - Disabled (or add kernel flag dart=0)

Note: Intel Virtualization Technology (VT-x) is supported by almost every Intel Sandy Bridge and Ivy Bridge processors. This is not the case for I/O MMU virtualization (VT-d).

Sources:

• How to set up the UEFI of your Hackintosh's Gigabyte motherboard
• Gigabyte Z77-DS3H Hackintosh - BIOS Settings

No DSDT needed!

Sources:

• Huge News! Gigabyte UEFI Sleep/Wake with NO DSDT! [TESTING]

Using version 5.5.5.

Check:

• UserDSDT or DSDT-Free Installation
• Audio / Realtek ALC8xx / Without DSDT / ALC887/888b / Current (read this if you get metallic sound after a while)
• Disk / TRIM Enabler (if you own a SSD disk)
• Network / Atheros - Shailua's ALXEthernet (can provoke rare crashes)
• Boot Options / GraphicsEnabler=No (if you own a natively supported GPU like the Nvidia GeForce GT 640)
• Boot Options / Verbose Boot (if you want to see what's going on)

Sources:

• Success: Mountain Lion Gigabyte GA-Z77-DS3H, i5 3570k Ivy Bridge, 16GB
• Loginfailed's Build - i7-3770k / GA-Z77-DS3H / 16GB RAM / 6850
• Experimental Atheros AR81(31/32/51/52/61/62/71/72) Driver for 10.7/10.8
• Gigabyte GA-Z77-DS3H Mac Install Guide

• If you want to boot on a 4K Advanced Format hard disk, check How to fix the boot0 error for your Hackintosh

sudo chown -R root:wheel MyKext.kext # owner: root, group: wheel
sudo chmod -R 755 MyKext.kext        # user: r+w+x, group: r+x, world: r+x

Using Geekbench, you should get a score (Intel Core i7-3770 @ 3.40 GHz) > 13000 (multi-core).

Do whatever you like, this is public domain.