Well done with your first game!
I'll write notes as I play, with some additional info, since you say you're a beginner.
Screen:
– You set the Newgrounds resolution in the project system way too large. To make it fit your game, I think you need to set it to 960×638 (600 height of the game, 38 Unity footer).
Menu, How to Play:
– In the fullscreen mode, it works fine, but the UI alignment and position is all wrong in regular resolution (I only see half of the screen). Check the Canvas anchors, assign them appropriately (e.g. the title to "Top", Back button to "Bottom Left" etc.). Also check the Canvas Scaler component (your elements should scale with the screen size). Then try to set the 960×600 resolution in Game View to see if it worked.
– Consistent capitalisation of letters…?
The Game:
Wow. Wow! This is amazing for a first game. It's a simple idea, really, but the little details you added make it all the more enjoyable. All the great particle effects, sounds and music help you avoid becoming bored quickly; but most importantly, you gradually introduce new kinds of enemies, so the players are hooked to see what's coming next. Shooting through several dots at once is also a nice effect.
Still, some things:
– The player spins around their geometrical center (i.e. including the cannon); but it'd look better if it spun around the center of the white dot alone. If it's a single sprite, moving its pivot could be enough (re-parent the transforms otherwise).
– Every text on screen has a different size, different font decoration and all of them are probably too large. Personally, I wouldn't let the "Score" occupy so much of the screen and move it under the highscore. And not use a number to represent the health (white dot icons instead). But this a matter of opinion and either approach is fine, even though it's at least recommended to stay consistent with the fonts.
– There's no temporary invincibility, so when you're surrounded by enemies when the game starts getting overwhelming, they're quite able to eat 3-4 health at once just because they all crash into you at the roughly same time.
If you'd like to change this, you could either add temporary invincibility, or (for example) lower the default max health, but create a small shockwave which destroys enemies in the immediate vicinity when hit to compensate.
But it's your game, you decide how (and if!) it's best to deal with it.
– The last new enemy I saw was the blue, fast one; so there are probably some I missed, but I thought it would be nice to include an enemy which doesn't approach you along a straight line which would make them harder to shoot. For example,
Curvy line: https://answers.unity.com/questions/363810/how-to-move-an-enemy-on-a-curvy-line.html
Spiral (equation): https://gamedev.stackexchange.com/questions/16745/moving-a-particle-around-an-archimedean-spiral-at-a-constant-speed
But overall, it's a good game; really well-made for a first-timer. Good luck with your second one!