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In argumentative discourse, persuasion is often achieved by refuting or attacking others arguments. Attacking is not always straightforward and often comprise complex rhetorical moves such that arguers might agree with a logic of an argument while attacking another logic. Moreover, arguer might neither deny nor agree with any logics of an argument, instead ignore them and attack the main stance of the argument by providing new logics and presupposing that the new logics have more value or importance than the logics present in the attacked argument. However, no existing studies in the computational argumentation capture such complex rhetorical moves in attacks or the presuppositions or value judgements in them. In order to address this gap, we introduce LPAttack, a novel annotation scheme that captures the common modes and complex rhetorical moves in attacks along with the implicit presuppositions and value judgements in them. Our annotation study shows moderate inter-annotator agreement, indicating that human annotation for the proposed scheme is feasible. We publicly release our annotated corpus and the annotation guidelines.