Dynamic analysis tools are often implemented using instrumentation, particularly on managed runtimes including the Java Virtual Machine (JVM). Performing instrumentation robustly is especially complex on such runtimes: existing frameworks offer limited coverage and poor isolation, while previous work has shown that apparently innocuous instrumentation can cause deadlocks or crashes in the observed application. This paper describes ShadowVM, a system for instrumentation-based dynamic analyses on the JVM which combines a number of techniques to greatly improve both isolation and coverage. These centre on the offload of analysis to a separate process; we believe our design is the first system to enable genuinely full bytecode coverage on the JVM. We describe a working implementation, and use a case study to demonstrate its improved coverage and to evaluate its runtime overhead.