These are the three enemies I haven't really worked out a solid strategy for (Besides "Kill really fast")
Kats will swoop in from completely off-screen, and if you put your shield up the moment you see them, you'll STILL get hit.
You can try sidestepping, but their placement and next course of action of either spit or chomp is random and difficult if not impossible to anticipate.
On their own, and with plenty of space, Kats aren't too troublesome, it's when they're mixed in with all the things a candlestick keep throws at you.
Greavers... thankfully I don't run into these very often, but every time I have, everyone starts dying, horribly. These have ended runs.
You cannot outrun these, they will stay on your tail, and trying to dash away will just get you lag-hit.
In any case I expect these, all I can really do is have my flourish handy and deal with them as quickly as possible.
Rocket Puppies.
Ever get those arenas where 12 of them show up around the parameter on top of menders healing and grenadiers throwing their crap everywhere?
I don't think anything more needs to be said on this one besides Fire, Tears, and Disbanded squads.
It's important to remember that you can interrupt a Greaver's attack by hitting them with anything. Bombs and Flourishes work well. Barrier items are useful for these enemies.
As for the 12 Rocket Puppies, you can dash to the side of the map (or use Shadow Cloak) and most of them will lose sight of you. Though this is ineffective if you're not playing solo.
**Edit**
You can dash through Kat projectiles without taking damage. Almost forgot about that...