The need that implies a desire to accomplish something difficult is the "Need for Achievement."

The Need for Achievement refers to an individual's desire to excel, overcome obstacles, and accomplish challenging goals. People with a high need for achievement are often motivated by a strong desire to accomplish tasks that require personal effort and skill. They seek out opportunities for success and are willing to take on challenging endeavors.

Need for Power: This refers to the desire to influence or control others and is not necessarily tied to the accomplishment of difficult tasks. Individuals with a high need for power may seek authority and control over others, but their focus is not on achieving difficult goals.

Need for Affiliation: This need is about the desire for social interaction, relationships, and a sense of belonging. It's not directly related to accomplishing difficult tasks; instead, it's about seeking companionship and emotional connections.

Need for Autonomy: Autonomy relates to the desire for independence and the ability to make choices without external constraints. It's not specifically about accomplishing difficult tasks but rather about having the freedom to act independently.

So, the correct answer is (2) Need for Achievement.