Perform, execute, discharge, accomplish, achieve, effect, fulfill are comparable when they mean to carry out or into effect.
Perform, sometimes merely a formal synonym for do, is more often used with reference to processes than to acts. One performs processes that are lengthy or exacting or ceremonial in character.
One performs acts that are distinguished or striking. When the end rather than the means to the end is stressed, what is performed is usually something undertaken or pledged.
One executes what exists in design or intent by bringing it into being or by putting it into effect. Sometimes execute is used in place of perform of a process involving great skill or a highly exacting technique.
One discharges duties or obligations when one goes through a required round of tasks.
Accomplish usually stresses the completion of a process rather than the means by which it is carried out. One accomplishes something begun or something which there is reason to expect. Sometimes accomplish implies the fruitfulness of effort or the value of the results obtained.
Achieve adds to accomplish the implication of conquered difficulties. One achieves a work, a task, or an enterprise that is of great importance and that makes unusual demands (as on one's energy, willpower, or resources).
Effect implies obstacles to be removed but, unlike achieve, it emphasizes inherent force in the agent rather than such personal qualities as daring and perseverance. Also, it is often predicated of things as well as of persons.
Fulfill implies a full realization of what exists potentially, or hitherto in conception, or is implicit in the nature or the sense of responsibility of the agent.