The first and foremost tip to surviving Big Shots is to keep track of your character. Trying to avoid the projectiles being fired from the cannons is all well and good, but if you take your eye off of your in-game avatar for too long, you might find your Fall Guy is dangerously close to the edges of the seesaw, be it in the back or one either side of the platform. This leaves you open for the slightest mistake or impact being enough to knock you off and eliminate you from the round. Some players have found dodging projectiles to be relatively easy, but things can get real crowded, real fast in a round.
Another helpful tip is positioning. Picking a center-left or center-right position between two canons is always a good policy due to the timing in which projectiles are shot out. Choosing these slightly off-center positions is also a good way to prevent you from falling off the side. The in-game seesaw’s movement is dependent entirely on the positioning of every player in the round. For instance, if a majority of players are rushing to the left, that is where the seesaw will lean.
Also, try to stay towards the front of the seesaw. If you get hit by a projectile, especially a bigger or faster one, it will knock you backwards quite a bit. Standing closer to the front gives you a small margin for error.