It's advanced in the sense that it's difficult to pull off. =)
In the way of ATs, my favorite is the Hyphen Smash. That's the sliding Charged Up Smash during a Dash. It can be done from a Stand-Still before the Dash animation even starts. You can do Reverse Hyphen Smashes, where you turn around just before the Hyphen Smash. The uSmash hitbox behind Luigi is larger. In about half an hour of pure Reverse Hyphen Smash practice, I was only able to do it once from a stand still.
There are Jab Cancels, where you tap Down after a Jab to quickly perform another move (or Jab without Tripple Jabbing).
There's the Fireball Lock, similar to Falco's Laser Lock, where Luigi spams Fireballs on an enemy lying on his back. It's rare because we rarely follow up Fireballs with Fireballs on the ground at close range. I don't know of any dTilt Tripping -> Fireball Locking...
Luigi also has a Zap Jump with both the Fireball and Green Missile. There isn't any height gain, but the Green Missile charges a tad quicker. I Tap Jump so I haven't gotten around to using them to great effect, if even possible.
Let's not forget the Jumpless Rising Cyclone which can save you in a pinch. You can rise out any (first) Luigi Cyclone even without a jump, but you need to have jackhammer fingers. The amount of lift you get from a full Jumpless Rising Cyclone is almost the same as one WITH the help of a jump's momentum, but human fingers aren't fast enough.
Taunt Spikes should count as an AT. Especially a Sliding Taunt Spike where you walk as you dTaunt to extend your range.
Speaking of sliding, you can also do Sliding Down Smashes the same way to slightly extend the range of your dSmash.
AT or not, Luigi also has the nice ability to Tech Land Fast Falls after any Short Hopped Aerial. Short Hop, Aerial, Fast Fall and immediately Air Dodge. It gives Luigi excellent Input Buffer during the Air Dodge.
And the last one that could be an AT is his Triple Aerial Short Hop. I don't know of any other character that can string together three aerial attacks during a single Short Hop. The "TASH" is fAir -> fAir -> nAir. The Sex Kick at the end will always connect Sweet Spotted.
I don't remember/know of any others.
