Energy isn't your problem. A tiny votive candle has enough chemical energy to blow up your house, if you could magically convert it all into mechanical work all at once. Mechanical power is the problem.
Mechanical power output is the rate of energy output over time, multiplied by the efficiency of the power supply (a dimensionless value between 0 and 1 that measures how much of the energy makes things move and how much of the energy just makes things hot). An efficiency of 0.3 is "good" for a well-engineered machine in good working order, so if you want the total power output including waste heat, multiply all the following numbers by 3 or 4.
Averaged over a few minutes, for a robot the same approximate size as a human, your power supply needs to be able to output about 5 watts of mechanical output power per 1kg of the robot or power-suit's total mass in order to duplicate the power output per unit mass of a human athlete. (This is about the mechanical power output of an elite athlete sprinting or cycling.)
To do a 1-meter jump-and-reach, it needs to achieve a vertical velocity of 4 meters per second, an output of 16 Joules per kilogram. It needs to do this in between 1/10 and 1/4 of a second, indicating a peak mechanical power output somewhere on the order of 100 watts per kilogram for momentary feats of athleticism like jumping and striking. This is a rough estimate of the mechanical power output of an elite basketball player doing the takeoff for a slam dunk. Much of the energy used by the athlete (or the robot) might come from spring-like energy left over from a previous smaller jump: energy momentarily stored in the slight stretching of the large tendons of the legs for the athlete, or perhaps pneumatics or even literal springs for the robot).
To lift a heavy weight as well as a human athlete, power probably won't be your issue. Muscles are force-limited, not output-power-limited. An elite weight-lifter doing explosive squat lifts has a power output of about 5-10 watts per kilogram body weight during the lift itself.
If your robot can move like a human athlete, it needs big feet: for every human mass of robot, you need a human foot equivalent of extra boot surface area. If it doesn't have big feet, it won't be able to get enough friction on the ground to do its athletics and it'll tend to sink into soft earth.