To solve this question, we need to find the option that is nearest in meaning to the underlined word "dodgy" from the given sentence: "The dodgy behaviour of the leader led to her fall."

The word "dodgy" generally implies something that is dishonest or not reliable. It suggests a sense of deceit or unreliability.

Let's examine each of the provided options to determine which best matches this meaning:

1. Principled: This word means having strong moral principles; upright and ethical. It is the opposite of "dodgy," making it an incorrect choice.
2. Dishonest: This word means deceitful or untrustworthy, which directly aligns with the meaning of "dodgy." Therefore, this is the correct option.
3. Dubious: This word means doubtful or suspect, similar to "dodgy" but not as close in implying dishonesty directly, making it a less suitable choice than "dishonest."
4. Painful: This word refers to something causing physical pain or distress. It does not relate to the deceitful or unreliable nature implied by "dodgy," so it is an incorrect option.

Based on the comparison and analysis of the given options, we conclude that the option "dishonest" is the word nearest in meaning to "dodgy."