We currently are on 15000 Milk spend, and only have 2335 left. Are we correct in needing several days of fighting boss battles 1-3 (for a total of 225 Milk per 6 hours) as the only way to get past that without buying Gems? Or are we missing another method to gain Milk? And one can only spend 5k right? Not 2500?

This took us by surprise, all other tasks were so easy up to this points and suddenly we got stuck. Gems apparently being our weakness. And to think we haven't been too lucky spending those for possible Epic cards. (Even got a journalist once, bah!)
Anyway, it has been fun up to this point!

Edit:

Hmmmm, reading some more posts on this "forum" we realise many others are already over a month into the event? For us it popped up rather out of the blue past night. Puts our question a bit in context. 

"easy", You have to open the chests to get 2 of the event cards to fuse them which mean +2k viagra and 8/16 hours of research so it stops you the first day unless you pay. (maybe it should work with other events... but it didnt worked with checkgirl)

This + the quest u says and probably others makes this a pay to play event.... or bad dissigned one.

EDIT:

there was different event last month, I started this one yesterday. And looks like events last for a month but u can only participate 7 days

same situation. If you don't want to buy gems to convert to tokens, then keep beating the first 3 bosses every 6 hrs and accumulate the tokens over the next few days. 

Then why is the quest "spend 17500" milk when there is nothing to spend milk on other than the 5000 chests?   That seems dumb.  Just make the quest 20000 milk, or 15000.

Ah, apologies Pedro, you are right. For us it seemed easy up to Quest 13 because we are months into the game. Our current amount of Viagra is over 63k, so that's a nice buffer. (Our highest was in the 220k we think, but then we got a few Epic cards to level 24 and also the Legendary Rider was finally up to 8 cards, and we are not as diligent in the adventure battles anymore so we haven't regained it.)

The speedy research was possible for us since we got a few examples of those speedboost items in June and August with mail from the developpers, and we never had a reason to use them until this event.

Thanks all for confirming, we just wondered if we were missing something. Like BitchPudding said, the 17500 task seems a bit silly when all we can use is 5k...

I feel you OP. I'm stuck there as well. At this rate (assuming I time it perfectly), I'm gonna need 48 hrs to get the next 5000 I need to open milk chest.
Afaik, the only way to accelerate this is to cash in on blue gems but I don't have much and wanna save it to get epic/legendary cards instead. I got the time, but I'm also not sure how long we got to complete this event. Did they say? I wanna get them all done before the event expires oof.

Yeah, this is a very poorly designed quest. They should have chosen an amount of milk that actually makes sense, and that can feasibly be obtained through quests. The event is practically going to end before we can gather enough milk for this quest. And in the meantime, there's not really anything to do. We'll barely be able to participate in the daily rankings as well, since we can't do any quests over the next few days...