Red-shouldered leaf beetle or Monolepta australis is generally only a sporadic pest in tropical and subtropical Eastern Australia. If you have a permanent population or if you are the route of a major migration it is unfortunate as they mass in large numbers and can cause destruction quickly. Other than supporting a general biodiversity including birds and beneficial insects that will predate on the beetle pests, the situation is usually so quick to develop that chemicals are required, to stop defoliation before it gets too bad and to hit the beetles before they move along.
Pyrethrum is very fast acting and might well be my first choice for a quick knockdown to stop the damage, although you might also try a neem extract product called Aza-max. The safest product of all is Entrust. It is developed from a biological agent and very safe, although not as fast acting as pyrethrum.
Both products mentioned are made by OCP - see
www.ocp.com.au
It is always hard to make recommendations without seeing the property or even a description, however if you are determined not to use a chemical, you may be able to use light traps as described in Bug. Only use them when the pest is flying and don’t leave it on all the time, as it will attract benign species too.