Since I was getting back into playing this a little bit at Funspot last weekend I'll offer as much help as I can...I'm sure Gorf Champion can add much more than I...
Space (Astro?)Invaders board:
If you fire right away you can normally hit the dispensing alien. I'm not good at shooting the space invaders while they are being dispensed other than the bottom row so if I get a few extra points by accident, it is luck. The rest of the board should be easy to clear even when the difficulty maxes.
Laser Attack board:
Usually I quickly destroy the closest enemy to my right upon entry and move back to the middle. Obviously dispense the boss enemies (with them there lasers) as fast as possible and the rest of the wave should be trivial. For God's sake stay out of the corners and be patient with the boss creatures.
Galaxians board:
IMO the toughest of the boards when the difficulty maxes. I usually play Galaga-esque and shoot as many enemies as possible as they are in formation prior to falling. I believe they are attracted to your current location (much like in Galaga) so I try to lead them where I have previously been as opposed to where I intend to go. Corners are the worst possible areas. I tend to move as far up as possible to not only get as many early shots away as possible while in formation but also to give me some leeway if I have to circle back and can move down as well as left/right.
Space Warp:
I can't explain how I play this really. Just move close to the hole

and fire on one side of the hole. Get to recognize the circle patterns and which enemies (if not destroyed) will circle behind you and which ones will just fly away normally. If they circle behind make sure you take notice so you don't get blasted from behind Phet.
Mother Ship:
Early levels I like to try and hit ship debris for points but when the difficulty maxes I try to get rid of the alien passengers first so they aren't interfering too much. Then I clear a hole in the barrier and use an "infinity" shape to dodge the missiles while also getting shots away and not getting trapped by debris. What I mean is I move from an top corner to bottom corner alternating sides method when I see the pause in fire (on max difficulty) while getting a shot away as close to the middle as possible without risking life and limb. Pretty hard to die this way I've found.
Good luck Gorfing it up.