Something that can only be accomplished with great effort is said to be a struggle. Martin Luther King, Jr. was a leader in the Civil Rights struggle. Alice Paul was a leader in the struggle for a woman's right to vote.
The verb form of struggle can be used for physical or mental effort. A police officer might struggle trying to detain a criminal or a student may struggle with a difficult algebra problem. If you scramble and climb awkwardly up something, you can also use the verb struggle to describe the action: "They struggled up the icy hill over and over again, so they could keep sledding."