The ACSM is awarded for 1080 days aggregated service in those theatres for which the GSM (e.g. Northern Ireland, Air Ops Iraq), an OSM (e.g. Sierra Leone or Afghanistan) or the Iraq Medal has been issued. An additional 1080 days is required for the award of the Clasp to the ACSM. More than 1 Clasp may be earned.
Separate criteria apply to Part-time members of the Ulster Defence Regiment (UDR) and Royal Irish (Home Service) Regiment.
Full details are laid out in DCI Gen 65/94 and, for the RAF, AP3392 Vol 4 Leaflet 2007 Annex B.
Off the top of my head I can't see how the ACSM is among the others, but I stand by to be corrected by a medal guru.