Alright, after my testing, here are my slight suggestions.
First off, this PSA is fantastic, and I know this is a beta. Improvements shall be made I'm sure, and here are my thoughts.
Slight flaw is the vulnerability Bomberman has during his air attacks, especially when hitting the ground during one. If I do a neutral A and hit the ground, I can get hit very easily for a move for such short range. Execution could be a tad faster too. I know he's meant to be weak physically, but if you can make his moves faster so we can space ourselves for the incoming bomb barrage.
His down tilt leaves him very, very open for a such a weak, no range attack. He sits there for about a full second or two before being able to move again.
Recovery from his dash could be improved. If you miss with it, you're going to get hit for sure. An extended hit box during the whole tackle would help, or getting up faster.
Now for the bombs. They're great. I only wish we could turn when throwing, in case you throw one facing the wrong way. The kick works great. Now I know we can just let it drop to explode, but I was wondering if we could make it detonate if we decide to just drop it, sort of like Snake's C4. I remember there was a power up that allowed you to detonate them at will. I think it would be a neat thing to do, if it is possible. It also would be neat if we could just detonate any bomb in advance before it automatically blows up by pressing B again, but I know nothing about the creation of a PSA so if I'm asking for anything complicated, simply tell me" no
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Last thing - the rocket recovery. Think you can make it do very, very light damage + pushback, like Viewtiful Joe's? He's mad open when trying to recover.
Great work so far, and I'm sure the Final Smash will be fantastic. I haven't experienced any bugs so far.