
Reksew_Trebla |
Faster than a speeding bullet might be easy. You just need to be able to dodge a bullet based attack as an immediate action. There has to be some way to do that. Failing that, you could try to be literal, and get your base speed high enough, coupled with run modifiers, like the Run feat, to make you able to run faster than a bullet can travel after being fired. Probably harder than the first option.
More powerful than a locomotive would be hard. You need to get your carrying capacity to be better than a locomotive’s, which is pretty high considering how much cargo they can carry.
Able to leap tall building in a single bound. I’m not sure if this one is possible. You’d have to get both your speed and vertical jumping to ridiculous levels to pull it off.
Anyways, I thought I’d propose this question to see if anyone has tried to make a build to do any of these before.

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1 and 3 are basically the same, if you go for move speed. Because for every 10' over 30' you get a +4 bonus to your acrobatics check, which in turn is 1' (running) high jump. I am pretty sure there is a build out there with a crazy high movement speed, but I can't remember where I saw it.
2, well, google says a locomotive can pull 27 million pounds (or 14,000 tons). Drag is 5x max load. A Colossal Quadruped can carry 24x the amount of a medium Humanoid. Ant Haul triples again. So 360x the normal chart. Horseshoes of Great Burden increase your carrying capacity by double. Burdenless Armor, increase each load(light, medium, heavy) by 50%. 1080x.
Muleback Cords increase your effective Str by 8, A traits to increase your effective Str by 2 for carrying, Muscle of the Society. Masterwork Backpack for another +1 effective Str. Heavy Gravity Acclimation Feat, +4 effective Str. Powerhouse Pelt armor, treat your Str as 8 higher. Str considered +23 higher.
And going +10 Str over the chart is 4x what is listed.
27,000,000/ 1080 = 25,000 lbs on the chart. /4 = 34 Str needed, reduced by 23 means you just need an 11 str, if you were a colossal quadruped and had all the things stacks.
I reserve the right to be incorrect on the math, but its the thought that counts.

avr |
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Cut from the air works on bullets. Or alternately there's teleport, ride the blast and similar ways to move a great distance rapidly.
Hefting very large amounts of stuff around has a long history - even pre-PF, partly due to a prestige class called the hulking hurler whose damage was based on the weight of the thrown object. Done.
The big guy used to just have the jumping thing, but it became flight rapidly. Flying is as you know very possible in PF.

avr |
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If actual jumping is required though - polymorph into a cerynitis for a 180' base speed. Cast cheetah's sprint. You may need silent/still spell to do this. With a move of 1800' you have a bonus of +708 to acrobatics for jumping before any other buffs or skill points, which should allow you to jump over reasonably tall buildings (1' per 4 points on the check).

haremlord |
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(Ignoring mythic, of course) Tenth level vigilante talent lets you treat a high jump like a long jump.
Leap and Bound (Ex) (Chronicle of Legends pg. 7): A vigilante with this talent adds his Strength bonus on Acrobatics checks in addition to his Dexterity modifier. He is always treated as having a running start when jumping, and his high jumps are treated as long jumps when determining the DC. When the vigilante jumps, he does not fall until the end of his turn, allowing him to attack or perform other actions in midair. If the vigilante grapples a creature capable of bearing his weight, he does not fall, instead remaining adjacent to the creature as it moves. A vigilante must be at least 10th level to select this talent.
As long as you can get your speed high enough and a high acrobatics score, you can get pretty high.