How to get past the giant snake in Trine 2

This is indeed a tricky jump, but I pretty consistently succeed in making it.

1. Start with a medium-to-long rope length, when you're at one extreme of the swing.
2. As you swing to the other side, shorten the rope until you're close to the platform - but not too close. In your screenshot above, a good distance will be equal to about half that platform's width.
3. Let go of the rope at around 80° angle - i.e. just a little bit before the rope becomes horizontal.
4. Keep the movement key pressed while in-air to try to land on it. Be careful, with narrow platforms it's also easy to overshoot them, not just fall short of them.

The number of swings before doing the attempt doesn't have any effect.

Technique 1: use the fireflies

The plants eat fireflies. Usually in the vicinity of the plants you find a swarm of fireflies flying around, and a lamp or two lying on the ground. Use telekinesis to move the lamp into the swarm to gather the fireflies, then move the lamp-with-fireflies into range of the plant. The plant will consume the fireflies and will then rest for a few seconds, ignoring you and allowing you free reign within its range.

Once the plant eats the fireflies, that trick cannot be used again until you gather up another bunch of them. You can reuse the same lamp for that (the plants only eats the fireflies, not the lamp). You can also reuse the same swarm of fireflies to recharge the lamp, those seem to never get exhausted.

Here's a video segment of someone feeding the plant - you can see the swallow and rest animation.

Technique 2: swing really fast

When Zoya swings with a long rope length she moves really fast. That is sometimes fast enough to swing past a plant. It's still risky, though.

Technique 3: fall through them

When you fall you move fast enough so that the plants can't get you. If you can engineer your movement through their range so that it's almost only falling down, you can occasionally get through alive.