I hear is pretty bad performance wise compared to the JVM for dynamic languages.
Thanks to the efforts of IronPython's creator, which eventually joined Microsoft for a while, the Dynamic Language Runtime (DLR) was created.
Eventually the JVM followed suit by investing into the infrastructure that eventually became known as invokedynamic.
Where most JVMs JIT compilers still beat .NET JIT compilers is that they explore more re-optimizations, while .NET JITs tend to only optimize once, but there are plans to at least improve this on RyuJIT.
https://en.wikipedia.org/wiki/List_of_JVM_languages
> To my knowledge it doesn't support dynamic types at all.
Not sure where you've got that from or what that's supposed to mean.
Perhaps he meant no dynamic languages have become popular enough on the JVM that it becomes common knowledge that the JVM can support popular types. None of those 4 languages you mentioned (Clojure, Apache Groovy, JRuby, Jython) are popular, whereas alternative JVM languages built from the ground up as static languages (i.e. Kotlin and Scala) are the ones people are adopting.
Reflection used to be used to implement dynamic types, but since Java 7 (2011) there's been a JVM instruction, invokedynamic, to explicit support dynamic types.