a Tail Tussle is usually how marsupilami's settle serious issues, and although females (especailly in South America, as that jungle isn't called the "Amazon" for nothing) can participate in these "fights", it's more commonly seen between two males. Since this is usually resurved for mating season, though exceptions are noted, the competitors don't really fight eachother, but merely show-off their skills.
Spinning- marsus balance themselves on their tails and spin the rest of their bodies, and whoever lasts the longest without getting tired or dizzy wins.
Whips- appearently, the winner is the marsu who can make the loudest whip-crack sound with their tail
Climbing- lassoing their tails on the most simularly-heighted trees or boulders found in such short notice, the winner is the one to get to the top fastest touching only their tails, and not what they're attached to (doing so of swinging up might get one disqualified).
Wreckingballs- this one is probaly their version of a game most humans call "chicken", in which the tails, tied in a fighting knot, swing at an object nearby the opponet, never attemping to hurt the other marsu, yet inflicting serious damage to that object (more often then not, a rock) in a way to sacre their opponent off-gaurd.