I dont think they will fire Shevchenko at all,they just signed his recently a few months back. I think they will keep him until the end of the season and maybe Genoa will in this transfer window sign some good players to actully stand a chance of not getting relegated.
Genoa has to do it if they want to stay in Serie A. 21 played only 1 win. they are very bad in defense, there have been 39 goals against them. of course a very bad achievement. I don't think it's just the defensive line that they have to improve. they also have to be strong in midfield to win the ball.