Usually when I do free for alls I find that the very worst spot to be is in the middle. Try to claim a corner and keep others out. Never get directly in the middle of the blob of players or you'll find you've taken a ton of damage in a very short time window. Even moreso since it looks like you main Bowser, who is a big target that attracts attention. Place yourself on the map wisely at all times. Always on the side, or outskirts. Never in the center. Let players come to you for a brief skirmish and that's where your skill can shine in and you can either kill them or scare them away.
Try to keep an eye on stocks. If one player seems to be doing a lot better, make sure to attack them. Don't let it creep up on you when suddenly everyone's out and they're still on their first stock. That's a recipe for trouble. I usually keep an eye on how everyone is doing and tend to try and bypass the losing players and target the one I think is going to potentially win. Grab and toss or knock people away who are on their last stock or who seem weaker and try to kill the player who's ahead! Otherwise you'll end up in a 1v1 where you're way behind on stocks or percent in the end. Try to plan how you want the end of the match to go. Who do you want to be left against you? Who do you think you can beat. Try to influence the match into the direction you want it to go so you can snag the victory at the end after the last 1v1 concludes.
Also be very wary of how punishable certain moves are in free for alls. I cannot count the number of times I've been hit by a ganondorf smash while jabbing or grabbing another player. Be very wary of your surroundings and keep tabs on everyone, not just your current target of interest. Staying alive in a free for all can require good situational awareness and caution. This works both ways, as typically I find it much easier to get off big moves like smashes in free for alls than in 1v1s where my opponent's attention is fully on my actions.