A Thoroughbred Monster is a monster with a complete family tree consisting of monsters of the same Breed. Creating thoroughbreds is specifically important in order to obtain the rare Arrowheads, Tigers and Mocchis in Monster Rancher Advance 2, but each one has different Class requirements.
Thorough breeding can be accomplished using a cable link as well on the Gameboy. You can raise the first two generations of your monster on the paternal side, and your partner can raise the first two on the maternal side. Then you can link and combine the monsters to create the Thoroughbred. Together it's 3 monsters apiece as opposed to 7 alone. Purebreed Monsters and ??? monsters work for this method, but regular sub-breeds do not.
Arrowhead Thoroughbreds[]
The main Arrowhead breed unlocked through breeding is Serket, and the others that become available after the process are Pa Bil Sag, Scorpion and Girtab. You can get these monsters prior to beating the Emperor's Cup as long as you have already unlocked Joker.
1) Raise a pair of Arrowheads to Class A.
2) Combine them into Arrowhead A and freeze.
3) Raise a second pair of Arrowheads to Class A.
4) Combine them into Arrowhead B and freeze.
5) Raise Arrowhead A and Arrowhead B to Class A and then combine them. This child is a Thoroughbred.
6) Raise a Joker to Rank B and combine it with the Thoroughbred. This will give you Serket and unlock the other three monsters at the Shrine.
Tiger Thoroughbreds[]
The main Tiger breed unlocked through breeding is White Hound, and the others that become available after the process are Cu Sith and Ifrit. You can get these monsters prior to beating the Emperor's Cup as long as you have already unlocked Gali.
1) Raise a pair of Tigers to Class A.
2) Combine them into Tiger A and freeze.
3) Raise a second pair of Tigers to Class A.
4) Combine them into Tiger B and freeze.
5) Raise Tiger A and Tiger B to Class A and then combine them. This child is a Thoroughbred.
6) Raise a Gali to Rank D and combine it with the Thoroughbred. This will give you White Hound and unlock the other two monsters at the Shrine.
Mocchi Thoroughbreds[]
The main Mocchi breed unlocked through breeding is Devi, and the others that become available after the process are DeviRosso, DeviVerd, DeviBianc and DeviAzul. You can get these monsters prior to beating the Emperor's Cup as long as you have already unlocked Zan.
1) Raise a pair of Mocchis to Class E.
2) Combine them into Mocchi A and freeze.
3) Raise a second pair of Mocchis to Class E.
4) Combine them into Mocchi B and freeze.
5) Raise Mocchi A and Mocchi B to Class E and then combine them. This child is a Thoroughbred; freeze for later.
6) Raise a pair of Zans to Class E.
7) Combine them into Zan A and freeze.
8) Raise a second pair of Zans to Class E.
9) Combine them into Zan B and freeze.
10) Raise Zan A and Zan B to Class E and then combine them. This child is a Thoroughbred.
11) Combine the Thoroughbred Mocchi with the Thoroughbred Zan. This will give you Devi and unlock the other four monsters at the Shrine.