[@The 42nd Gecko]

Well, that's a big bunch of numbers, and as far as the abridged version of Newtonian Mechanics go, you can say that. I just want to say it's not really the true numbers you'd use on college level (read:true) Physics class. Let me see if I can make some sense of it all.

1º Force (Newtons) is: Mass (kg) x Acceleration (m/s²), thus the force behind the jump would be of: 30.000 kg x 9,81 m/s² (gravity's acceleration when close to Earth's surface) = 294.300 N.

2º You mistook Pressure (Force/Area), with pure Force. Let's consider the tip of that sword as having a very small area, making it really sharp (for mecha standards), so 1mm radius, to an area of 3,14x10^-6m², divide the previous force for that and you have= 9,37x10^10 Pascal, or 93,7 Gigapascal or 924,8 atm (approximately the pressure of a 94m deep dive in the sea).

3º That one is a lot more complicated. If you decelerate a 44m/s object to 0m/s in a time that tends to zero (can't use Calculus w/o a function, so lets assume 01 milisecond for the time), you would get: 44.000m/s² negative acceleration x 30.000 kg = 1,32x10^9, or 1,32 GN. Which is far less than your estimate, but close to 4.500 times the force the mech can generate from gravity alone. I'll not add pressure for this, since it would vary wildly based on the area of contact between the mech and whatever was hit by it.

4º Now, I'll jump directly for the main issue, energy liberation. Which on the previous case would be of 29x10^6 Joules. For the kick, it would be hard since I can't be sure of Juno's speed, since Juno weights around 60 kg only, if she moved at say mach 5 (really freaking fast) for around 1.500m/s, it would be: 67,5x10^6J, or 67,5GJ, far less than a nuke. But the pressure would be tremendous.

A direct hit from Juno is not a waste of energy, like an explosion (which damages you via pressure), it's force applied with precision to generate the maximum damage. It's hard to compare those scales, anyways, that's a better application of actual Physics.