The sketch on the right is one of the earliest ones to show a tetrapter. Well, they used to be called 'tetropters', but the 'Naming Authority' decides that that was a mistake, and now they should 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 is that of an animal moving a bit like a helicopter, and that is indeed what tetropters look like. They have four wings, just like the tetrapterate flyer coming up to the tetropter, but there the similarity ends. Tetrapterates are similar to birds, but with four wings of course, and their wings 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 in 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.

The scheme shows how tetrapter wings move. They each move to and fro over a quarter of a circle, and near the end of the circle they rotate along their long axis. The wing next to it does the same thng but in mirrored fashion, so the two wings move up close together and then are pulled apart. This is the so-called 'clap and fling' mechanism of generating lift that is used on Earth as well. Earth fluers only have two wings, so there is only one 'clap' for each movement cycle, but tetropters with their four 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. Tetropters are excellent at hovering flight and they are extremely manoeuvrable.

Different tetrapter species move their wings in different ways. In this 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 something more like 'rowing', in which the wings beat down over a considerable distance. The result is a bit like an oar pushing gainst 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 flash its wings to attract potential mates. Flashy, isn't it?