In regards to the Warmonger trophy, second wave battles do count but the training tent battles do not. Getting Warmonger on hard difficulty will be tough as those fights will leave you pretty battered and second waves will be very challenging.
I did my first playthrough blind on normal difficulty and managed to get a fair chunk of the trophies but most notably missed High Spirits & Warmonger...it sure felt like I did 40 battles, but I must have been just short.
My second playthrough was on hard and I attempted those 2 trophies along with the others I missed the first time...I quickly realized I was not going to get Warmonger and I misunderstood how High Spirits worked, so I had those 2 leftover.
My third playthrough was on easy and I decided to keep track of my battles and had no problem hitting 40 battles and keeping my morale up.
Hope that helps.