Under rating threshold (hideshow)
Progression for the hard badge: Day 1 (first jump): +17$ on 5', buy acc. 1; D2 (stay horizontal to get distance achievement): +25$ on 5' & dist. 1(+25$), buy glider 1; D3 (get max height 1 + duration 1): +49$ (=(16+22)*1.3) on 5' & max height 1 (+25$), duration 1 (+25$), buy height 3 & acc. 2; D4 (get max height 2 + duration 2): +122$(=(31+50)*1.5) & max height 2, duration 2 (+100 * 2), buy rocket 1 and air res. 3; D5: get ~100$ and speed 1 on 5', buy fuel 3; D6 (max height 3):+324$ (=(126+51)*1.8) on 20' & max height 3 (+500$), buy height 6, acc. 4, air res. 5; D7 (glider 2): ~300$ on 20' with duration 3 achievement (duration bonus ≥ 1.9), buy glider 2; D8: finish 10' with ~500$, D9: get max height 4, duration 4 and 1000$ to buy glider 3. With glider 3 bought before day 10 you can easily get the badge (I got it on day 17, day 16 is possible with this progression).
Under rating threshold (hideshow)
I just found a bug that makes the hard badge easy... Step 1: Watch animation of penguin walking to the ramp. Step 2: Go to another tab on your browser when your penguin jumps. Step 3: Wait for 4-5 seconds then enter the game again. your penguin will have accelerated as if the ramp was actually that long. got glider on 1st jump and rocket on second.