To beat the dungeons (assuming Advanced Logic as basic logic includes other requirements such as hearts, swords, bottles type of stuff):
EP - Bow and Lamp/Fire Rod - Lamp will cover it completely. Fire Rod only works if big key is not vanilla location.
DP - Glove, Lamp/Fire Rod, Boots (potentially if a key is on the torch), weapon to kill Lanmo
ToH - Lamp/Fire Rod (pending Big Key in basement), Weapon to Kill Moldorm
PoD - Hammer, Bow, Lamp
SP - Flippers, Mirror, Hookshot, Hammer
SW - Fire Rod, Sword
TT - Hammer/Weapon to Kill Blind - Hammer dependent upon key logic for the dungeon's small key
IP - Mitts, Fire Rod/Bombos, Hookshot, Cane of Somaria, Hammer - Cane and Hook are very key dependent. Complicated key logic goes into which or both if necessary
MM - Flute + Medallion to get to Mire area and open front door, Hookshot/Boots to get in, Lamp, Somaria, Weapon to Kill Vitty
TR - Mitts, Hammer, Medallion + Sword to get in, Somaria, Fire Rod, Ice Rod.