I think "amateur" gives the wrong impression; it makes it sound as though anyone can have a go. A novillada is a proper bullfight in a bullring, like a corrida except that the bulls are younger ("novillos", aged 3-4, hence the name), and the fighters are bullfighters in training who have not yet taken the "alternativa", graduating to being full professionals and thereafter only fighting full-scale bulls.

"Picada" means with a picador (the guy on a horse with a lance whose job is to weaken the bull at the start). There are also "novilladas" without a picador, so this bit ought to be reflected. The word "picador" is reasonably well known and I think it can be used as is, without further explanation.

I would be inclined to keep the Spanish term "novillada" and add a translation in parentheses. I think "novice bullfight" could be used: both the bulls and the bullfighters are novices.

http://www.cas-international.org/en/home/suffering-of-bulls-...

"What is a "novillada" which I sometimes see on the posters?
This is a bullfight involving young bulls and young matadors who have not yet moved onto the full sized bulls."
http://www.gomarbella.com/whatson/bullfighters.htm

"The bullfights you are most likely to see in Puerto Vallarta are real bullfights with real bulls, but technically you are more likely to see a novillada (novice bullfight)"
http://books.google.es/books?id=PXxG4RTmPgAC&pg=PA94&lpg=PA9...

"He followed the novice bullfight circuit, waiting for a chance to break into the novilladas."
http://books.google.es/books?id=76zMU6DtQioC&pg=PA163&lpg=PA...

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Note added at 1 hr (2014-03-31 09:59:12 GMT)
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If you do keep the Spanish term, it should go in italics.

Maybe better "novilladas (novice bullfights) with a picador", rather than "with picadors", since it's one picador per fight.