First of all Love the game. Fantastic and smooth animation, a derivative story (Kill Bill) but told very nicely, through the campaign and the Prequel co-op. I really like 2D brawlers and games like God of War, Devil May Cry, so I enjoyed this game as a genre fan. What did you guys think? Is it too mashy? Is it enjoyable? 
But coming to my main question... I'm trying to beat the game on hard. Are there any tips or tried and true weapon combos that are efficient in most situations?

Been going back to the chainsaw a lot since it can kill most normal sized enemies with a quick grab attack.  Also the katana takes almost the whole life bar with a pounce attack.  Since most of the enemies have increased health on hard being able to quickly isolate and kill before you can be swarmed under is key.  Also judicious use of the moment of invulnerability when your block dashing can save your hide.

I find the chainsaw to be the best weapon although the katana is useful because you can impale (grapple) all sizes of enemies (except for bosses) and it automatically throws them away from you which can be useful in 1v1's against larger foes (after a group of smaller foes has been killed) to launch them off an edge.
 
As HeroicDrinkingSong said, use dodge a lot and try to group enemies instead of having them on either side of you. 
 
Shotgun + Chainsaw = epic

I've been digging the chains lately. At first I didn't see the point, but they seem to do a lot of damage, especially on the bigger guys. 
 
 I fear for Hard mode *shudder*

I personally set my self the challenge of getting 200 kills with every weapon, which I achieved a while back. [Next stop - 500] I recommend doing the same as you get to understand the strengths and weaknesses of each weapon and may end up liking one you didn't at first. If you can easily pull of fast combos and have enough skill with dodging/dashing you should pull out the Machete and Uzi combo every now and again. The Uzi grapple is does a pretty good job as it deals a decent amount of damage and then kicks them back giving you some room. [Also if you don't already have the red & white ninja costumes I recommend the Machete/Uzi set up for getting high combos easily.] I used the chainsaw and shotgun for most of my first play through but haven't touched them much since, unless the screen fills with the big guys and I need to blow them away. The Katana is sometimes useful but the lack of having a proper grapple means I don't use it much for that, I just use the standard swipe attacks. The chains I pretty good for damage, but I tend to only use them against the big enemies. I mean its all preference obviously, I personally switch weapons a lot mid battle, depending on the situation so I don't really have a favourite. 
 
Also to answer your other question, no I didn't find it mashy, but then I don't really mash at the buttons. I'm sure you could easily get through most of the normal campaign by mashing though, apart from maybe the last boss.  
 
The advice given above about the invulnerability during the block dash is also extremely useful when tackling hard difficulty.