Bullhorn of Plenty

So I will explain how to do this: First you will get some [item=237774] for completing a match, you will receive some of them (sometimes I received 3 of them) in the chest what spawns if you finish a match. Once you receive 5 of them enter an other match, once entered start killing all the trash because it won't let you use the item before you clear the arena. Once you killed all the trash simply click on the item in your bag and some mobs will spawn, the CD on the item is 30 seconds, so you should go slow on killing the bosses during the match so you are able to use 5 [item=237774] in a single match. The followup achievement requires 10 [item=237774] used in a single match and after that 15 (!) [item=237774] used in a single match, so you need to use the wheels on the ground for sure to extend your timer.

Note: Sometimes one of the NPCs use [item=237774], I don't know if it counts towards the achievement or not, better just have the needed items in your bag. If you can't find [item=237774] just type it in the textfield in your bag.

Followup achievements: Bullhorn of More Plenty and Bullhorn of Most Plenty

I can confirm that the Boss Cogs that say that you've summoned more Reinforcements do count towards the achievement.

As DPS Paladin using the NPCs as my group.

I used the [item=237774] to knock out all 3 achievements by using it 15 times in one match.
Bullhorn of Plenty - used 5 times
Bullhorn of More Plenty - used 10 times
Bullhorn of Most Plenty - used 15 times
Boot Hill create 30 tombstones. Die 30 times. You will see statues piling up on the left and right. Make sure there are at least 30 (do more to be safe).

As soon as I killed the trash, I used the [item=237774] every 30 seconds and clicked every gear on the ground.
The entire arena was full of bosses and reinforcements.
I slowly started killing each one including the 3 Goblin Zappers and dying as fast as possible to get my 30 deaths.

45 minutes later, I was able to finish and the [item=240199] was in the chest.