If you are upgrading Virtual Appliances, check out our procedures for an "expedited" upgrade that brings you immediately to the latest version, without needing to stop at any intermediate version: Expedited Appliance Upgrade - CA API Gateway - 9.3 - CA Technologies Documentation
(Note that this works only with virtual appliances; it does not work with hardware appliances or software Gateways.)
The topic "List of Update Files" describes all the platform updates that must be applied when upgrading from various versions:
List of Update Files - CA API Gateway - 9.3 - CA Technologies Documentation
It is important to note the distinction: The Gateway update itself is "cumulative". That is, you can install the Gateway 9.3 update patch on a Gateway 8.3, without needing to install 8.4, 9.0, etc., first. However, it is the platform patches that are not cumulative. And the further back you go, the more platform patches must be installed.