Yeah, it multiplies damage, score and most firing rates of enemies. Damage and score are the same multiplier, which doesn't have any particular formula to its values, whereas firing rate is linearly dependent on difficulty, going from 80% at baby mode :c to 150% at
EPIC MAN MODE >:C. (and of course is at 100% on Normal)
Because i'm such a silly person who likes tables, here's a handy table to refer to.
So as you can see, the potential DPS rises more or less exponentially. Perhaps i should make score dependent on that and not just damage?? (as if anyone actually looks at the score right now, might end up removing it entirely)
Also, with a lot of defensive upgrades, you can survive a surprising amount of shots on EPIC MAN MODE >:C, since you can, with every defensive upgrade active and at full strength, achieve a damage reduction as high as 98,4% (and that's without counting the shields hitpoints, which against a standard laser brings it up to 99,1%) for a moment.
The shield points become less significant against a large laser, that won't matter a lot since a 98,54% damage reduction still trivializes pretty much every shot that strikes you. Yellow beams are a bit trickier, however, since they ignore shields and do 15 base damage. If you don't have your defensive skills maxed and time your forward movement right, a shot to the face by a yellow beam on EPIC MAN MODE >:C hits you for 120 damage, which means you die.
The most notable exceptions to this are the giant beams and collision damage. Giant beams deal 100 base damage at the moment, modified only by difficulty, meaning that if you're playing on anything higher than Easy, you'll die instantly (because getting hit by a beam that's as wide as your ship tends to be bad). Even if you're playing on baby mode :c, they are by far the biggest hit your ship will take short of being rammed by a sufficiently large enemy (which is ALWAYS an instant kill).
The only enemies that kill you instantly on collisions are the bosses, the Despoilers and the Leviathans. As long as you don't actively fly into the face of the first two bosses, you probably won't experience that, and the Despoilers only pose a collision threat because of their large size, since they move as simply as most other ships (BUT they have giant beam weapons). Leviathans are a different matter, however, in that they will CONSTANTLY try to ram you until you finally destroy them. They might well be one of the biggest recurring threats to your well-being on the lower difficulties.
Also, regarding collisions, it's worth noting that non-fatal collisions in v0.9 CAN be mitigated by the shield (which they couldn't before), however they hit the shield twice as hard as shots do. This may make you think that hey, collisions hurt you more through the shield! But nope, math says it'll always be at least a slight reduction in damage, since the base shield gate is 50%. It's just not as effective as it is against shots, since the shield wasn't designed to cope with ship collisions.
So yeah, the only perfect defense is to not get hit. Later on, difficulties MIGHT change more things, but don't hold me up on that.
Edit: Bonus fact: if we were to make a difficulty where every shot fired by any enemy would kill you at all times despite every concievable form of defense, the damage percentage would have to be 125875%. Any damage taken that is less than 5 base damage is survivable, however, but that's probably not going to happen very often. Either that, or we add a boolean value that says "kill player y/n", which is also possible.