Here are some career defining innings of Bill O'Reilly vs England (Didn't include SA and NZ for obvious reasons):-
In Melbourne; 30 Dec 1932:-
O'Reilly got 10 wickets in this match; 5 in each innings. In the 2nd Innings, he got the wicket of Sutcliffe and Hammond pretty cheaply (33 off 53 and 23 off 43 respectively).
In Nottingham; June 08, 1934:-
O'Reilly got 11 wickets in this match. The 4'fer in the 1st innings included Cheap wicket of Hammond (25 off 79) and a pretty important wicket down the order of Patsy Hendren (79 off 247).7'fer in the second innings included the wicket of Sutcliffe (24 off 102) and Hendren (3 off 45).
In Manchester; 06 July 1934:-
Got a &'fer in the first innings, which included pretty important wickets of Hammond (4 off 2), Sutcliffe (63 off 135) and Hendren (132 off 248).
In Melbourne; Feb 26, 1937:-
Got 8 wickets in this match. Got a fifer in the first innings, which included the wicket of Hammond (14 off 54). Got another 3 wickets in the second innings, where he got Hammond (56 off 106) again.
In Leeds; July 22, 1938:-
Got his final 10 wicket in a match in this match. Got fifer in each innings. In the first innings, he got Hammond (76 off 149) and Compton (14 off 36). In the second innings he got Hammond out for a golden duck and also got the wicket of Compton (15off 20).
Individual batsman vs Bowler stats are incredibly hard to find, but O'Reilly got the wicket of Wally Hammond 10 times in test cricket. Pretty impressive I'd say.