As per request
Here we see Zilla Jr.'s atomic breath blast Cyber-Zilla hundreds of meters into the air.
I used RowVid for this.
It takes 12 frames from the moment Cyber-Zilla is hit for his entire body to disappear above the screen in the shot immediately afterward.
Specifically, I started counting from this frame, the first frame to show the atomic breath making contact with Cyber-Zilla:
25 frames = 1 second, so 12 frames = 0.48 seconds.
He obviously rose a distance greater than his tail length, which we know from the official guidebook is 78 meters.
Velocity = 78 m / 0.48 seconds = 162.5 m/s (lowball)
The blast was in contact with his face for 6 frames. I started counting from the frame above and counted up to this following frame:
6 frames = 0.24 seconds
Acceleration = (162.5 m/s) / 0.24 s = 677.08 m/s^2
It was discovered on Wikizilla that the guidebook for the 1998 GODZILLA movie never states that the 1998 Godzilla's weight is 500 tons. In fact, there seem to be no official sources supporting this number.
The only statement for a 1998 Godzilla's weight comes from a scene in the episode "Cash of the Titans" stating that Zilla Jr. weighs 60,000 metric tons.
I'll assume Cyber-Zilla, being of the same species but with mechanical enhancements, also weighs 60,000 metric tons = 60,000,000 kilograms.
Force = mass * acceleration = 60,000,000 kg * 677.08 m/s^2 = 40,624,800,000 Newtons
Putting This Much Force In Perspective
This much force, exerted over just 0.24 seconds, would be enough to send over 284,000 metric tons 60 meters (Zilla Jr.'s height in the theropod stance) into the air against gravity!
According to this, the height of a projectile shooting straight upward is represented by the formula
distance = (vf^2 - vi^2) / (2*g).
Sending a mass 60 m into the air:
60 m = (0 m/s - (vi)^2) / 19.6 m/s^2
60 m = (vi)^2 / 19.6 m/s^2
vi = (60 m * 19.6 m/s^2)^1/2 = 34.29 m/s
An object would need to reach a speed of 34.29 m/s to move 60 m upward against gravity.
(34.29 m/s) / 0.24 s = 142.875 m/s^2
40,624,800,000 N / 142.875 m/s^2 = 284,338,057.74 kg ~ 284,338 metric tons
In other words, Zilla Jr.'s atomic breath during this feat would have been strong enough to blast Biollante or even Bagan off the ground after just under 1/4th of a second of contact, and Cyber-Zilla took this to the face!