You can see the location of the new boss on the map at the end of the video. Note: You have to have beaten all the bosses including the new TV boss to enter the new area.

Location for the second new boss (TV Boss).

Here is a video I made showing the secret room that gives the birthplace achievement. Alternatively, you can find the room by following the green orb thing that you can free from the secret room hidden under the waterfall found in the room after the elegy boos fight.

I found a secret corrupt boss rush mode which doesn't put you at one health but takes away healing, abilities and chips.