You can use the Trigger In and Trigger Out port of an ILA core to cascade these two ILA cores.
Turn on the Trigger Out mode in the front ILA and set the trigger condition for this ILA.
Set the behind ILA to capture only when there is a trigger in event.
You could also OR the trigger in signal with a condition on the counter if you needed to.
To start the capture, arm the behind ILA first, then arm the front ILA. When the condition is met both ILAs will be triggered.