The plot of instantaneous power of the Dirac function
The problem becomes as I try to calculate the power in time domain, $P(t) = \left\lvert\delta(t)\right\rvert^2$

As you figured out yourself, that's impossible: the power of the Dirac impulse isn't defined, it diverges (goes to infinity).
Hence, you especially can't plot the power &quot;correctly&quot;; it's zero anywhere but at $t=0$, where it diverges.
But quite honestly, this should come as no surprise: you can't correctly plot $\delta(t)$, either (the value at $t=0$ isn't defined just as much as its square isn't).
So, whatever question can be answered by that plot: I'm afraid you'll have to find a &quot;better&quot; question.