"Dude, Where's My Gar?" contains the following tropes:
Ambiguous Situation: The appearance of the Teen Titans Go! Beast Boy is one since he appears on a television. Is this the "real world" where the show exists, or given that the characters often show some Medium Awareness is this just reflecting that and is actually the Go! reality?
Broken Pedestal: If the events of "Doom Patrol" didn't already do this, Gar learns that Dr. Caulder is responsible for the deaths of his parents and many others.
The Cameo: Many in Gar's trip across the multiverse:
Et Tu, Brute?: Downplayed in that the Chief isn't present in the scene, but Gar is horrified to learn that the man who saved his life also killed his parents.
Fusion Dance: Dominic uses his powers to fuse a scientist with an ape who is dying of the mysterious virus, so that they will die together.
The letter that Gar reads is addressed to Avery Sunderland, expressing Niles Caulder's disinterest in The Green and Swamp Thing.
Freedom Beast calls Gar "The Changeling", which is Beast Boy's grown-up alias in the comics.
Refused the Call: Gar is told that he is to be the new Guardian of the Red, and that he must abandon the Titans to do so. Gar declares that that is not happening.
The Reveal: Caulder engineered the outbreak that killed Gar's parents and nearly killed Gar himself, only to save Gar as part of his plan to eventually achieve immortality.
Wham Shot: When Gar sees the signature of Dr. Niles Caulder (a.k.a. Chief from the Doom Patrol and the man who saved him from the Green Plague) on documents in the lab that created the Green Plague.