A 'food chain' is when you feed the first piece of food to a critter that is then immediately eaten by the critter behind it. This mainly happens when you feed a fly to a medium (green/red) critter that is directly in front of a big (purple/pink), but it also will happen if you feed a critter of either size that is in front of a bomb or electric critter (as these are omnivorous). You do not need to finish the level to get this trophy, it will award as soon as you trigger your 10th food chain of that level.
Note that it is impossible to move critters around to 'set up' a food chain, as you cannot yourself place a critter into the proper position. If you try to put a medium critter on a large one it will eat the critter, whereas if you drop a medium onto a large via popping intervening critters, that creates a combo, not a food chain. Thus the ability to make a food chain in a particular location is a property of the board as it spawns (and can only be destroyed by you, not created), so you want to watch for anywhere a medium critter is in front of a large one.
This trophy may happen naturally over course of game even without you trying for food chains specifically (especially on some later levels that take a long time to complete). However if you want to get it sooner you can aim for this directly on one of the earlier levels. Scan the level and look for every situation where a medium critter is over a big critter and use a fly to trigger the food chain. Note that many times multiple medium critters will be in front of the big critter, just remove all but one and then get the food chain. On an easy level (you will probably want a wide board, and all colors in play) your biggest enemy will be completing the level too soon, so you can intentionally avoid picking up the jewels that drop to ensure your hunger bar fills more slowly. If you keep those tips in mind 10 food chains is a snap.