The lack of Item room isn't as well compensated by the starting items when compared to the other challenges. Isaac also doesn't start with an active item.
Shops can sell Mom's Purse, allowing a second trinket or Smelter allowing the tick to be smelted and new trinkets to be picked up.
Shops can also sell Hive Mind, which will make blue flies and blue spiders bigger and stronger.
Isaac starts with one item each for the Spider baby transformation and the Beelzebub transformation. Meaning two more items from each set will give Isaac a marked advantage. While the lack of treasure rooms somewhat limits the possibility of completely either transformation, it is still possible:
The aforementioned Hive Mind counts for both transformation ( just the Beelzebub transformation), and is in the shop pool.
The only other shop item that's in the spider baby set is Spider Mod.
For the Beelzebub set, the only other item in the shop pool is Jar of Flies, which synergies well with Hive Mind.
Plum Flute, another Beelzebub set item, can be easily acquired by not attacking Baby Plum for about 30 seconds.
Skatole, another Beelzebub set item, can be won from shell games, which is likely to spawn in arcades. Arcades can only spawn on even numbered or XL floors, and only when Isaac has more than 5 cents. (Having more than 2 keys means the arcades may be replaced by vaults however)
Key masters has more than a dozen fly items that contribute to the Beelzebub set that he could pay out with.
You still produce flies when firing at a lowered Hosts, so it is possible to farm flies off of them