There is a growing interest in applications that utilize continuous sensing of individual activity or context, via sensors embedded or associated with personal mobile devices (e.g., smartphones). Reducing the energy overheads of sensor data acquisition and processing is essential to ensure the successful continuous operation of such applications, especially on battery-limited mobile devices. To achieve this goal, this paper presents a framework, called ACQUA, for 'acquisition-cost' aware continuous query processing. ACQUA replaces the current paradigm, where the data is typically streamed (pushed) from the sensors to the one or more smartphones, with a pull-based asynchronous model, where a smartphone retrieves appropriate blocks of relevant sensor data from individual sensors, as an integral part of the query evaluation process. We describe algorithms that dynamically optimize the sequence (for complex stream queries with conjunctive and disjunctive predicates) in which such sensor data streams are retrieved by the query evaluation component, based on a combination of a) the communication cost & selectivity properties of individual sensor streams, and b) the occurrence of the stream predicates in multiple concurrently executing queries. We also show how a transformation of a group of stream queries into a disjunctive normal form provides us with significantly greater degrees of freedom in choosing this sequence, in which individual sensor streams are retrieved and evaluated. While the algorithms can apply to a broad category of sensor-based applications, we specifically demon- strate their application to a scenario where multiple stream processing queries execute on a single smartphone, with the sensors transferring their data over an appropriate PAN technology, such as Bluetooth or IEEE 802.11. Extensive simulation experiments indicate that ACQUA's intelligent batch-oriented data acquisition process can result in as much as 80% reduction in the energy overhead of continuous query processing, without any loss in the fidelity of the processing logic.