The sketch on the right is one of the earliest ones to ever show a tetrapter. In fact, these animals used to be called 'tetropters', but the 'Naming Authority' decided that that was a mistake because the Greek for 'four'is 'tetra', meaning that the erstwhile 'o' was not just a vowel put there to string the various words together, but part of ann important word. Hence, the animals should now be called 'tetrapters'. But old habits do not die easily, so you may still encounter 'tetropter'...

There is not much detail to be seen, but the impression of this sketch is that of an animal moving a bit like a helicopter, and that is indeed what tetrapters look like. They have four wings, just like the tetrapterate animal in the background approaching the the tetrapter, but there the similarity ends. Tetrapterates are somwhat similar to birds, but with four wings of course, and their wings do not have feathers but are built of bone, muscles and subcutaneous bubbles. In contrast, tetropters are much smaller, insect-like, and their wings are membranes. The most important difference is however the mode of flight: tetrapters are radially built animals and have four wings that each beat clockwise as well as counterclockwise.
Tetropters have been discussed various time in the blog: I would start here, then read this one, followed by this post, to end here.

Here is more about tetrapter flight. They also have a unique way of walking. At first sight, you would think that they walk like spidrids, that after all also have eight radial legs. But tetrapters divided their eight legs into two groups of four, with one set of smaller legs that move inside the circle of the larger ones. The two sets resemble the front and hind legs of four-legged animals, in that they have a different anatomy.

This scheme shows how tetrapter wings move. Each wings moves to and fro over a quarter of a circle. Near the end of the circle the wings rotate along their long axis. The wing next to it does the same thng but in mirrored fashion, so the two wings move close together, swing upwards, and are then pulled apart. This is the so-called 'clap and fling' mechanism of generating lift that is used on Earth as well. Earth flyers are bilaterally symmetrical, so there is only one 'clap' within each movement cycle, whereas tetropters, with their four radial wings, have a 'clap' twice in each wing cycle: it's a 'double clap and fling'(DCAF).

Here is a more developed animation, showing a nondescript sphere, but moving about as a tetrapter might. Tetrapters are excellent at hovering flight and they are extremely manoeuvrable.

Different tetrapter species move their wings in different ways. In this particular scheme the wings hardly move down while beating to and fro, and so they stay nearly horizontally. The lift is all due to aerodynamic effects of air moving over the wings.

This tetrapter uses a pattern more like 'rowing', in which the wings beat up and down over a considerable distance. The result is a bit like an oar pushing against water.

The turning of the wings can have interesting colour effects, because the wings catch the light differently depending on their angle. This bright red tetrapter makes the best of the low light, when the sun sets, to present its wings to attract potential mates. Flashy, isn't it?