+1, ASI is good for everything and the Brandishes have useful charge attacks so CTR is also good stuff if you use it.

Monster type bonuses are probably a matter of taste, but bonuses against Undead and Fiend are a waste since you shouldn't have to use a Shadow-type weapon against them unless you derp on equipment setup and have nothing else.
The relative desirability of bonuses for neutral vs. bonuses for vulnerable monster types depends on how much your sword is used for each. If you use it almost exclusively against Slimes and Gremlins, (like if you have weapon slot upgrades and/or use only swords) and/or if those monsters just give you the most trouble, then those bonuses are the best Monster damage bonuses. If you use it a lot against Constructs or Beasts as well, especially if you feel you could use a bit of help there, those bonuses might be better.

For example, I use only two weapon slots and like to combine Nightblade with Magnus since the gun creates safe openings for the sword when dealing with Wolver packs. Thus, a bonus vs. Construct would round out my capabilities best there. OTOH, before becoming attached to this synergy I combined Nightblade with Kilowatt Pulsar and thus the most desirable monster type bonus I could have for the sword would be Beast. These preferences would both be reversed for a player who tends to focus on maximising strengths rather than minimising weaknesses, so it depends a lot on many variables in how you like to play.

Again, I agree that ASI is good for every one; you can dodge or shield sooner after attacking AND you can pour on the DPS faster. What's not to love?

edit: IOW, if for any reason your Acheron is only considered for Slimes and Gremlins then those are the only monster type bonuses that benefit you. If OTOH you use it against neutrals like Constructs and Beasts, preference depends on whether you'd rather gain bonus damage for a third monster family or boost one of the existing two.