Shadow Gigalith

Best PvE Offensive Moveset

• Smack Down is the quick move of choice.
•  Meteor Beam* is the top choice. Rock Slide is okay if you don't want to wait for another event or drop an Elite TM. 
• Mud Slap isn't as useful.
• Solar Beam and Heavy Slam lack type-synergy and lag behind as a result.
• Super Power lacks synergy on offense.

Best PvE Defensive Moveset

• Mud Slap is generally the better choice for defense because it hits so many types for Super Effective damage. That said, Smack Down does too!
• Rock Slide is the move of choice next to Mud Slap, as Rock and Ground are fairly synergetic together.
• Heavy Slam and Super Power can fit with either Fast Move, though they may tend to be a bit less effective.
• Meteor Beam* has a lot of power behind it, but its high cost means that Shadow Gigalith probably won't get a chance to unload it.
• Solar Beam is painfully slow. If Shadow Gigalith gets it off, it will hit hard and basically delete many Water or Ground Type counters, but that's probably not going to happen.

Smack Down is superior to Mud Slap in terms of damage output, not to mention STAB, but the latter offers extra coverage. Both have the same energy generation. 

Rock Slide is a strong charge move that gets STAB and offers relevant coverage. Superpower is a bit risky to use due to its self-debuff effects, but its valuable coverage and respectable damage can be worth it if played correctly.