I managed to achieve what I was trying to do:
Issue issue = client.getIssueClient().getIssue(issueKey, null);
client.getIssueClient().update(
issue,
ImmutableList.of(new FieldInput(IssueFieldId.ISSUE_TYPE_FIELD,
ComplexIssueInputFieldValue.with("id", id))), null);
This will change the type of the issue, hope this will help anyone else who encounters this problem.