I finally figured out the answer to my question.
I should've looked at the API's a little more thoroughly but I also found some other forum post that gave me an idea.
for(testStep in testCase.getTestStepsOfType(com.eviware.soapui.impl.wsdl.teststeps.WsdlTestRequestStep.class)){
assertList = testStep.getAssertionList()
for(assertItem in assertList){
logSaver(testStep.getName() + " - Assertion :" + assertItem.getName() + "--" + assertItem.getStatus())
error = assertItem.getErrors()
if (error != null){logSaver(error[0].getMessage())}
}
}