Mini bosses are in the lowest table, Level 1, and cycle through 5 unique bosses.
When you defeat the third boss, The Cephalopod, you will pop the achievement.
Watch out for the first boss as his telepathic throw can gutter your ball instantly.
Tier 1 is unique in that it doesn't have one boss, but many. Every time you kill a boss, it advances down the list in the order given. Once you've killed them all, the list repeats and the boss colors shift. Killing bosses also gives you multiplier, and sometimes adds a portal to the drain which will warp your ball to Tier 2
Every boss shoots bullets when hit. Some also have other behaviors, which are noted below.
Hermit: Will telekinetically throw the ball when hit. Deceptively dangerous, as there's nothing you can do about the telekinesis. Creates a drain portal on death.
Soldiers: Actually many small skeletons in a regular formation. Hitting one from the front violently repulses the ball, but a hit from the back is an instakill. Easy and relatively safe; if you can keep one on the right side alive, you can avoid the more dangerous bosses while keeping the shots which ascend you to T2 clear. Creates a drain portal on death.
Cephalopod: A dangerous eldritch horror. Shoots a huge amount bullets in a 360 formation when hit. Great for farming coins, but also relatively weak; dies in only a few hits. Upon death, triggers a multiball. Creates a drain portal on death.
Homunculi: A three-headed homunculi. You receive a multiball for this boss, which is good, as hitting it sometimes temporarily creates a gravity well directly above the drain. An incredibly dangerous boss for this reason, so don't be afraid to take your time to make sure your ball remains safe.
Goat: A demonic-looking goat with many eyes. Hitting the goat can make the eyes pop out, causing a pseudo-multiball. This can be a bit disorienting (Not sure what the eyes are used for yet, if anything. Sound off if you know!)