The feats in SMBZ involving Yoshi's Island were already re-calc'd here, but I feel the slight inconsistent sizing of the characters and objects in the series makes it the method used to get the sizes of the mountains and Yoshi's Island not the best. The pixel scaling itself is fine though which is good since it's currently 2 AM and I really don't feel like pixel scaling everything all over again so I'm going to re-steal AidenBrooks999, DreamcrosserSquad & Psychomaster35's measurements
Instead I'll use the numbers listed by the VsBattles Wiki as the minimum for snow-capped mountains. Seeing as Yoshi's Island is typically portrayed as a tropical island, I'll use the 4600 meter tropical snowline.
E[]
The Breaker Beam[]
Lowest Snowline Height = 4600 meters = 235 pixels
Left Mountain Height = 447.5 pixels = 8,759.57446809 Meters
And now we simply plug these new numbers into the previous recalc
Left Mountain Height = 8,759.57446809 Meters = 410.5 pixels
Left Mountain Radius = 149 pixels = 3,179.4801358 Meters
Middle Mountain Destroyed Diameter = 324 pixels = 6,913.76888589 Meters
Middle Mountain Destroyed Height = 233 pixels = 4,971.93873584 Meters
Right Mountain Destroyed Diameter = 268 pixels = 5,718.79648586 Meters
Right Mountain Destroyed Height = 185 pixels = 3,947.67667867 Meters
Left Mountain Volume = (1/3) * Pi * 8,759.57446809 * 3,179.4801358^2 = 92,730,768,519.3 M^3
Middle Mountain Volume = (1/3) * Pi * 4,971.93873584 * 3,456.88444295^2 = 62,219,155,323.4 M^3
Right Mountain Volume = (1/3) * Pi * 3,947.67667867 * ,859.39824293^2 = 33,800,216,800.3 M^3
Total Volume: 92,730,768,519.3 + 62,219,155,323.4 + 33,800,216,800.3 = 188,750,140,643 M^3 = 1.88750141*10^17 Cm^3
Vaporization of rock is 25,700 Joules/Cm^3
1.88750141*10^17 * 25700 = 4.8508786*10^21 Joules, 1.15939 Teratons of TNT, Low 6-B, Small Country level
A very nice upgrade and very consistent with Mecha & Eggman surviving the Death Egg's planet shaking crash/explosion
Yoshi Island Go Boom[]
First the Mountain Volume
Left Mountain Height = 8,759.57446809 Meters = 418 pixels
Middle Mountain Height = 554.5 pixels = 11,620.0575181 Meters
Middle Mountain Radius = 221 pixels = 4,631.2582714 Meters
Right Mountain Height = 507.5 pixels = 10,635.1292884 Meters
Right Mountain Radius = 172 pixels = 3,604.41820218 Meters
Right Mountain Middle Diameter = 255.5 pixels = 5,354.23750382 Meters
Middle Mountain Total Volume = (1/3) * Pi * 11,620.0575181 * 4,631.2582714^2 = 260,996,628,765 M^3
Right Mountain Total Volume = (1/3) * Pi * 10,635.1292884 * 3,604.41820218^2 = 144,691,073,980 M^3
Subtracting the previously destroyed volume from the total of each mountain
Total Volume: (260,996,628,765 - 62,219,155,323.4) + (144,691,073,980 - 33,800,216,800.3) = 309,668,330,621 M^3
Now for the island itself
Mountain Middle Diameter = 5354.23750382 Meters = 127 pixels
Island Upper Diameter = 482.5 pixels = 20,341.8865795 Meters
Island Lower Diameter = 795 pixels = 33,516.6835869 Meters
Island Height = 132 pixels = 5565.03425594 Meters
Calculating this as a conical frustum gets 3.2328427*10^12 M^3
Assuming 50% hollowness
3.2328427*10^12 * 0.5 = 1.61642135*10^12 M^3 = 1.61642135*10^18 Cm^3
1.61642135*10^18 * 25700 = 4.1542029*10^22 Joules, 9.92878 Teratons of TNT, 6-B, Country level
Sonic Goes Fast[]
Sonic scales the leftmost mountain in ~8 seconds
This mountain has a height of 8,759.57446809 meters and a radius of 3,179.4801358 meters, which gives the side Sonic scaled a length of 9,318.75736 meters
9,318.75736/8 = 1,164.84467 Meters/Second, Mach 3.39605, Supersonic+
Not as fast as their current speed rating, but a good supporting feat.
TMS Range[]
getting Mecha's range with his energy attacks
Island Diameter = 33,516.6835869 Meters = 597.5 pixels
Energy Blast = 470.6 pixels = 26,398.24485 Meters, Tens of Kilometers
Island Diameter = 33,516.6835869 Meters = 595.5 pixels
Screen = 860 pixels = 48,403.6068593 Meters
And the blast covered the screen well before it reached the peak of its size, so I'll double this
48,403.6068593 * 2 = 96,807.21372 Meters, Tens of Kilometers