Guild Wars 2

Is it possible to do World 2 without the slingshot or bomb?

Yes, it is. I rarely use it to begin with and i think on my first playthrough i probably didn’t. In any case i see no reason why it wouldn’t be possible.
The freezing bananas are a pain without ranged, but a bit of dodging and even those are simple.
The torch however you will need.

No, it isn’t. You can’t shoot down the ice pickles in world 2 zone 3 without a range weapon.

To be able to do w2-z3 you HAVE them and 400 baubles to buy the torch in the first part of the level.

You also need it for some achievements (like bauble master in 2-2).

The turtles/alligators in Zone 1 many times need Slingshot/Bomb to reach.

Hard block in Zone 3 for bombs to knock down ice shards to jump onto.

It’s possible to do it without them on Infantile mode (rainbows skip all the puzzles where they’re needed), and if you find the flute songs in W2Z2 and W2Z3 (infantile) you could theoretically do it without them on normal mode as well.

However, getting the flute song in W2Z2 requires bombs as well, so…

slingshot has ranged dps better than nunchucks
i can kill king toad in 2 rounds of attacking with it

but you dont need it anywhere, and its requirement that you be on the same level as the enemy is sorta frustrating.

bombs are great for killing things that are gonna annoy the hell out of you and are the only way to get the secret rooms
but no i dont think i needed bombs… anywhere. so far.

you should buy them anyways. theyre excellent and youll have enough bobbles.