I'm no electrical wizard, but I can speak to some of the hazards that go with using extension cords.
When you send electricity from point A to point B through a wire, you will lose voltage due to the resistance of the wire itself. Think of it like losing momentum when you ride a bicycle into the wind. The farther you travel, the more energy you lose. It is the length of the cord that matters here, not the distance you're covering with the cord. If you use a 100' extension cord to cover a 10' span, you're still making that electricity travel 100 feet, and losing voltage accordingly.
If you lose enough voltage in transit, you can cause damage because the thing you're trying to power is demanding more power than can be delivered. For example, think of connecting your pool pump to intakes in the pool with 1/2" pipe, or a garden hose, or something smaller. If the plumbing can't deliver sufficient water fast enough, you'll do bad things to the pump, right? So in order to use extension cords safely (in ANY application) there are two things to keep in mind: 1) Use the shortest practical cord to get your power from point A to point B, and 2) make sure the gauge of the cord (i.e. the diameter of the conductor wires inside) is sufficiently large to keep up with the demand at the load end.
I've never seen a Tiger Shark in person, but from the pictures I see on the web I suspect it's powered similarly to my Blue Diamond, which uses an outboard power supply plugged into the 120 volt AC power source, with the robot being plugged into the power supply. The power supply is really a transformer that converts power from 120 AC (standard household current) to 12 or 24 volt DC for use by the robot. This is not a power-intensive process. In my opinion (and please remember that I am NOT an expert), this is not a terribly heavy electrical load.
Most of the cheap, orange extension cords you see in home centers are 14 gauge (sometimes even 16 gauge, smaller wires still), which is sufficient for powering average sized hand tools, smallish motors, etc. When you want to power something bigger, like air compressors, power washers, table saws, things with larger motors, you need a heavier cord (12 or sometimes even 10 gauge).
If you want to learn all the gory details, google on the term "voltage drop". You'll get more than you ever wanted to know. Power loss associated to voltage drop is very uniform (i.e. for a given conductor diameter, you will lose a constant amount of voltage over a given length). For example, say that for a given wire length and gauge, you'll lose 10 volts to voltage drop. If you are sending 100 volts down the line, you're losing 10% of your voltage. If you send 1,000 volts down that wire, you're losing the same 10 volts to voltage drop, but it's now only 1% of your total voltage. Transmitting 10,000 volts costs you only 0.1%, and so on. This is why power companies use transformers ramp the voltage up incredibly high, to tens of thousands of volts, when transmitting electricity over long distances, and then use different transformers to bring voltage back down to consumable levels at the other end. This is also why you need to get the heck away from power lines when they are on the ground.
If you only need to cover 20 feet with the cord, I suspect a 25', 14 gauge one will do you just fine. Try it, and keep track of the condition of the cord. If it starts to feel warm after powering the robot for a while, look for a heavier gauge cord. And of course, make sure that you're only using the cord across a dry surface. It's a pool deck, after all... but if the pavement is wet, keep the cord off it.
