You dont need any traps, just press B (if on xbox, idk about nintendo or playstation) when you defeat an enemy and you wont trap it and will just claim bounty and exp. Traps are only necessary if you wish to play as the Villains that you defeat in Skylanders Trap Team. When you defeat a Villain, they are transported to the Villain Vault.
So you are saying to fully enjoy this outing, I should have at least: 1 mini, 8 different elemental trap skylanders, 8 different elemental traps, and 1 giant? And that will allow me access to ALL challenges, and ALL areas of the game? They also make villain battles easier. I know this from firsthand experience, since I got Trap Team used and only had figures from Spyro's Adventure and Giants for a while. So yeah, you don't need a Trap Master (or traps) to just play through the game.
However, I am pretty sure you at least need the Traptanium portal. You don't technically need any traps to play and finish the game, as all villains that you defeat are automatically trapped back at the Skylanders Academy in the "Villain Vault" in the center. However, it is a lot more fun and opens a lot more content to use the villains and traps as intended.
Unless I've miscounted, there are more traps than actual enemies that can be trapped. As well as that, there are some in-game variant enemies that can ONLY be trapped in specific traps. I know that you'd need one of each element, at least, and a Kaos Trap, but are there any other specific traps I'd need? Before playing Skylanders Trap Team, you will need to pick up one of the new Starter Packs.
There are two versions you can choose from when playing on one of the many consoles, but only one. Can you beat Skylanders Trap Team without traps? No. In order to play through the game, defeat the final boss and let the credits roll, you do not need one single Trap.
This is a common misconception for those that are new to the game. Traps are only necessary if you wish to play as the Villains that you defeat in Skylanders Trap Team. You can play as all the villains with 8 traps, plus the extra 3, provided you take time to switch them in the villain vault.
You don't any traps to defeat the villains and send them to the villain vault. Like the regular Starter Pack, the Dark Edition comes with the Water and Life traps, but also the Ultimate Kaos Trap - a larger, rarer version of the standard Kaos Trap, which allows players to capture Skylanders' notorious villain.