In the Christmas Episode, Zach and Ivy use a bit of subliminal manipulation to lure Carmen into a trap. Knowing that Carmen had already had two narrow escapes, they'd left a clue suggesting, ostensibly, the White House Christmas tree. However, the message used the phrase, "Skating on thin ice". Knowing that after a couple of close calls, White House security would be a bit too daunting for even Carmen Sandiego, and the tree at Rockefeller Plaza in New York would be an ideal famous tree for Carmen to nab, Zack and Ivy laid in wait for her there.
Carmen then gets a moment of her own for still being able to make off with the famous tree.
Carmen giving Lee Jordan an earful after he flings Zack and Ivy into the ocean. You do not threaten children, especially not these two in particular, in front of Carmen Sandiego. Also heartwarming, since it demonstrates the odd bond between Carmen and the two detectives.
Judge R.B. Traitor presses one of Ivy's Berserk Buttons when he threatens to jail Carmen without a trial. Ivy, strapped by steel restraints to a heavy steel chair, manages to stand up while protesting the lack of jurisprudence, straining at her restraints the whole time, and looking like she very well could burst them.
In the same episode, Zach and Ivy engage in a bit of MacGyvering, making an atlatl from a busted chair, flinging a spear, which damages Carmen's escape vehicle while, at the same time, providing a zip line for Zach and Ivy to quickly get from a tower to the ground and take out the villains.
Of particular note, Ivy uses her flying kicks to take down R.B. Traitor, a man who is quite muscular and at least twice her size, if not more.
Any time Ivy demonstrates her leg strength. In the first episode, as well as in "The Remnants", Ivy manages to kick open doors held shut by thick pieces of lumber. And in "Retribution Part 2", she manages to free herself from a pillory just by flexing her legs.
Earlier in "Retribution Part 2", Carmen constructs a Viking longboat solely off a postcard image reference.