The rules of the Jungle game I've played on the internet are:

Each player moves one piece in turn.

Only one animal may occupy a square at a time. An animal may eat any weaker animal from the opposing side by moving onto its square. The one exception is that the rat may topple the elephant (by running into one of its ears and gnawing on its brain). When animals of identical strength meet, the moving animal eats the stationary one.

Only rats may enter river squares. A rat is therefore immune to attack while in the river, except from another rat. A rat may not attack an elephant from the river, though it may attack another rat in this way.

A lion or tiger at the edge of a river square may leap the intervening river squares and land on the nearest jungle square beyond. Any animal occupying that square that it could legitimately attack is destroyed. However, if a rat (from either side) occupies one of the river squares in the line of the animal's jump, the jump is blocked.

The red trapped squares on each player's side may be freely entered and exited by that player's animals with no penalty. An opposing player's animals lose all power on entering an enemy's traps, and are automatically weaker than any other piece.

Each player has a den which must be defended from the opposing player. No animal may be moved into its own side's den. If any player's animal enters the opposing player's den, that player wins the game.