Each checkpoint can have 1-3 different goals you need to reach before moving into the next checkpoint. Below you can find some tips on how to collect different goals.
Balloons - these are collected when they float away from the screen. On some levels, you can also find balloon boxes that will release multiple balloons when hit. Those balloons will be anchored into a block with a rope, so you will need to break the rope by flinging a bird through it.
Cages - these need to be dropped to the ground to break them. If the cage contains a hatchling, it get's collected as soon as the cage breaks. If the cage contains another level goal, such as a Firefly, then the normal collection style for that item applies once it gets freed.
Pigs - these need to be popped by causing damage to them. You can pop them instantly by hitting them directly with the birds. You can also cause damage to them by dropping them or dropping blocks on top of them.
Fireflies - these lovely fellows come in pairs! Your goal is to break the blocks that are keeping them separate. As soon as the route is clear, they will fly to each other.
Frozen hatchling - the hatchling needs to be released from the ice block by using the light source and the mirrors to melt the ice. To allow the light to travel through the mirrors you will need to make sure there are no blocks in the route.
Mystery Box - while this item itself is not a level goal, it can however contain one! The boxes can contain different items, ranging from regular building blocks to TNT, extra birds, or level goals.