If your car is running weak that probably has nothing to do with the battery or its connections. Once the engine has started, power to run the car (and recharge the battery) will come from the alternator. If the starting is weak, that could be a problem with the battery or its connections.
That connection looks pretty corroded. But the best way to be sure if the resistance is excessive is to measure the voltage. With the engine off and a decent electric load (headlights, cabin heater, windscreen heater) on, current will flow from the battery but there should be no measurable voltage between the chassis and the negative battery terminal.
Similarly with these loads off and the engine running the alternator will send charging current to the battery but there should be no measurable voltage difference between the chassis and the negative battery terminal. As an additional test or if you don't have a voltmeter, you can use a jump lead to connect the engine block to the negative battery terminal. If there is any change in engine sound (indicating a change in charging current and hence engine load) it means the ground connection is poor and some of the charging current is going through the jump lead to bypass it.
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I had a problem with starting a few years back. As soon as the solenoid kicked in the instruments would go dark, and the solenoid disengaged. Then the cycle repeated once a second. Battery voltage was fine, even with the headlights on. However at one point when I touched the negative terminal with a single meter probe, a spark flew out! I knew I had found the problem. There was clearly a voltage difference between the battery post and the clamp.
I actually measured 6 volts between the battery post and the clamp with the headlights on. So I removed the clamp, cleaned it and reassembled it. Problem solved.