Since there are many connected crumbling tiles, your best bet is to avoid them at all costs except of dying. Just jump on the normal tiles, and you will soon find yourself beating this level.
The Child can walk across the first line of crumbling tiles without falling off. Afterwards, the lines are short and disjointed. Don't be afraid to jump to them, since they will not crumble. Then again, since the Child doesn't crumble the crumbling tiles, there has to be a twist. With the factor of speed considered, the Child has worse manoeuvrability than the Skater. Find a regular tile connected to or one-tile apart from the chain of crumbling tiles, and upon landing on it, jump, and hope for the best.
The Runner is able to dodge the crumbling tiles in general, since the whole chain is single-use. Stay in the middle of tiles to avoid slipping up.
The Skater goes very fast, zipping through the level. Again, each chain has one use, so be sure to use it wisely. When near the crumbling tiles, switch to shorter jumps, for control and to hit a wall if the jump is quite clearly going to go wrong.
Overall, this level shouldn't be too hard, and no prior experimenting is required.