In the Glasshouse Entrance:
"Is the number up for these guards?" is your first riddle here. Simply scan the guards that are already dead on your left when you walk into the glasshouse and you're done.
In the Botanical Glasshouse:
"What time is tea time in Wonderland?" will be your next riddle. Just head over to the left side of the big fountain and look for the planter there. You'll see a tray that has a tea set on it and it will complete the riddle when you scan it.
In the Statue Corridor:
"Remember the Waynes? How could anyone forget?" is your next one, and you just have to find the benches here with name plates. Zoom in on them until you find the one with the Wayne's names on it to complete the riddle.
In the Flooded Corridor:
"The Ratcatcher needed more than just charm to lead his army." For this riddle, you have to crawl through the vent after the wonderful Joker will block your way. While you're doing this, look down through the grates that you come across and you'll see the Ratcatcher's costume below. This will complete your riddle.
Then, you'll hear "Looks like all the king's horses trampled all the king's men." Just find the benches and zoom in on them to find the wooden soldiers that are broken on top of one of them.
Next, you'll get the riddle "Is this s tribute to what a mad dog left behind?" and you just need to find a statue with no head and zoom in on the plaque on it that's been vandalized.
In the Aviary:
"There's no closet in the gardens, so someone is using the roof instead." While this one is a weird one, you simply have to sneak past the Joker's mobs and climb up the wall on the left. When you get to the top, you'll come out right across from the control room that you need to head toward. While you're headed toward it, look over to your left and you will see a drop. Down in it, there is a skeleton that is hanging out, just zoom in on him and you're done.
In the Abandoned Chamber:
"This challenge can only be seen by those with a different view on life." is your last riddle here in the Botanical Gardens. To finish this, get to the door that is at the top part of the chamber that heads to the final room. Go to your left and climb across the wall, then head to the middle of the room and look over to the platform that's on the left side of the door. (This is the same platform that you had to use to get to the part of the wall that you climbed across just now.) You'll see part of the "?" that you need on the platform that you're on, and the other part is on the lower one. That will complete the last riddle here.