Second Chain Stage Strategy,
For me personally I RUSH to get every key off the bottom about 2 inches up as soon as possible seeing that the birds can now fly all the way to the bottom and its not worth the risk later in the level when everything is going on. So after getting everything up about 2 inches its all learning where is safe with the birds and watching out for the snap jaws coming down. I always do the 4 middle keys first then the first key and finally the last key last seeing as its always a close call with a bird turning the corner sharp. You should picture JR in a square, between the birds flying and the snap jaws coming down you need to be in a "safe square". Thats what helps me in the level. Move slowly and do not rush, you do not always need to get 2 keys up at a time and you do not always need to finish a key after you start moving it.
Springboard stage
My general gameplay involves me double jumping to platform, and getting to the left platform. Then climb the 2 vines until you can switch one vine to the right. This would mean I have one hand on the peaches vine & one hand on the vine to the right of it. Now if you look at the vine with the apple, I wait for a bird to get slightly above the ball (on bottom of vines) and then grab that and am able grab it and shimmy to the next 2 vines, wait on those 2 vines and am able to judge when to move next to the last peaches vine, Then wait for the bird to cut the corner sharp on the turn and go across. Then jumping over the gap while jumping one bird and then quickly jumping to the vine with the apple. Then waiting for a gap and making it to the key while jumping a bird at the end.
Note: I usually dont go for the fruit on the vines unless I am feeling frisky, It usually costs me lives
Second Spring Stage, on top platform.
Jump the gap between the platforms when there is a small break in the birds. Quickly Jump and grab the vine with the apple. You can use that to kill 2 birds if timed right. Wait for the small break in birds and slide right down, Then continue to jump Straight up and holding left while in the air so that when u land you take a little step. Jump straight up and repeat untill you get the next break in birds and run forward and jump to the last vine. Timing is key in jumping and dont take a full step between the birds or they might run into you.
For marios hideout I have to do it as soon as possible..
~Jump and grab the vines, climb up and jump off, clear the blue spark and grab fruit in same jump, dash to the end and climb up.
~Second plat - wait for the yellow spark and jump up, wait about 1/4 of the way on that platform and a blue and yellow spark will come at that point and you need to jump those together, then run across and grab the vine (the blue spark will look like its gonna hit you but you just make it below it)
~The third platform I have no pattern for, I play it by ear every time, usually wait till theres only like 2 blue sparks loaded and NOT on the first (closest) vine.
~The last platform you jus need to jump the yellow spark once, and the last jump is always a close call.