In Treno's auction house bid to win 10 items, best to wait until he says "Any more?" then place a bid (stand in front of him) and you should win.
Note that four items are for another achievement (Sword of kings) which you need to win and sell on:
Une’s Mirror - Sell this item to the Nobleman at Cafe Carta.
Griffin’s Heart - Sell this item to an Adventurer at Cafe Carta.
Rat Tail - Sell this item to an Adventurer at Cafe Carta.
Doga’s Artifact - Sell this item to the Scholar that resides at the Synthesis Shop.
If he says they are going to take a short break, just go out and come back into the auction house. Oh and have ALOT of gil first, I'll have to come back later on.