So I just completed three of the most grindy achievements, all in duels:
1) 'Buff 600 minions with Invigorating Sermon': Playing Duels with the hero power that summons a dude and adds one to my hand (to be able to generate more buffing targets), it took me 3 deep (to 5 or 6 wins) runs to get the full achievement. In 2 out of 3 runs I was able to pick a 2nd copy of the spell from a bucket. Also in 2 out of 3 runs I discovered the passive treasure where I discover a spell when I play my first holy spell in a turn. Sometimes I discovered more copies of Invigorating Sermon this way (or via Snack Run too). It will feel very slow at first, but when on the 8th or 9th game in a duels run your deck is big enough that casting Sermon once can often buff 30-40 minions, especially if you played First Day of School and/or a spell that summons 5 dudes right before
2) Deal 150 extra damage with Nature spells: I don't even have 'Bru'kan', but he is not needed. Cheap source of spell damage (Rune Dagger, Primordial Studies, Imprisoned Phoenix, Bloodmage Thalnos) is good enough. If your goal is to win then blasting their face with multiple Lightning Bolts and so on is good, but the spells that really help you make a lot of progress with the quest are the AOE ones. I had 2-3 occasions where the opponent went really wide and I was able to cast a Lightning Storm with spell damage +2. That's 2 extra damage on each minion you hit and helps a ton with achievement progress.
3) Summon 250 Imps: That was the easiest. Playing Warlock with soul fragment synergies and the passive HP that summons an imp every time you shuffle fragments into your deck (and picking up soul fragment buckets along the way) made it very easy to complete this in just 2 deep runs with Warlock. First one I went 11-3 actually and summoned already 200/250 imps
One more thing. For the priest achievement with Serena Bloodfeather, since the card is total garbage and you don't want to play a deck with her I suggest you also do it in Duels. Just put her and Animated Broomstick in your deck and wait till you draw both. Should be fairly easy in the first 1-2 rounds where your deck is quite small, especially with the heal/draw hero power. Repeat 4 more times and achievement done
Just my 2c on these achievements: For the Warlock achievement where you have to summon a ton of imps, by far the easiest way is to play duels with the passive hero power that summons an imp for every soul fragment card played (I like doing achievements in Duels in general so that I don't have to tank my rank in constructed, but this particular one is way easier there).
Also for the Hunter Achievement with Tavish Stormpike, it is easy to complete by just grinding and playing beast-heavy decks with him, but I have the following cool meme idea (which I haven't managed to execute yet). Build a deck with Tavish, Tame Beast Tundra Rhino as your only 5-cost beast, and a bunch of 1-, 2-, 3- and 4-cost beasts. The combo needs only 5 mana but you need to wait till turn 10 to upgrade Tame Beast to rank 3. Then you play Tavish and Tame Beast which summons a 6-costed 6/6 beast with rush, this triggers a summon of Tundra Rhino, followed by a chain reaction where all the beasts you summon have now charge. You can get 6 beasts summoned in one play and potentially OTK the opponent
Oh and Duels was also very helpful with the Kolkar Pack Runner achievement where you need to summon 6 Hyenas on a run where I discovered the treasure that gives you 3 coins;)