If he's still at Mark II ships on the tech tree, the AI Progress can't be that super high -- although the difficulty is 3, so that has a big effect on making the "take everything" strategy not quite so suicidal. In an 80 planet map I generally take around 25-30 planets at diff 7 and rarely hit the Mark III enemy wave tech level.
General tips:
- Keep your longer-ranged ships (cruisers in particular) further back from your other ships, and they'll survive longer while still pounding the enemy to paste.
- Take only the planets that will actually be worthwhile, rather than trying to take them all. The upper difficulties will kill you quickly if you act too aggressively. For more information:
http://arcengames.com/mediawiki/index.php?title=AI_War_-_AI_Progress#When_To_Worry- Using a tech like a Mobile Repair Station, or engineers along with your fleets, or Mobile Force Fields along with your fleets, can make them last far, far longer than they would otherwise.
- Missiles up the AI Progress, and so should really only be a last resort, or used in specific circumstances (when clearing wormholes with lightning missiles, for instance).
Bear in mind, also, that these are just general truths and not hard rules. There are exceptions to every rule, and if you want to play the game differently than it was designed, that can be quite valid. I know some players on a 100-planet map who are 40+ hours into a campaign and are trying to take every planet. It's a challenge, because the AI Progress gets to be incredibly high, but sometimes those sorts of oddball challenges can be the most fun -- I've certainly done that sort of thing by getting 12 hour games out of Empire Earth islands maps, for instance, myself.
Hope that helps!