Here is the full list of all 20 Swinging-Man achievements.
Beat 1st loop without upgrade card
Upgrade Bullet-Time to level 3
Fully upgrade perks
Beat 4th loop
Beat 3rd loop
Travel in the air for 1,000,000 meters in total
Upgrade Magnet level 3
Shoot 6,969 bullets
Beat 2nd loop
Kill 4th boss
Kill 3rd boss
Kill 2nd boss
Upgrade Liquid Bullet to level 3
Kill 3 enemies within 1 second
Collect 10,000 nudies in total
Kill 1st boss
Don't touch the ground more than 30 seconds without slinger.
Reach the moon
Reach satellite
Reach first boss in 120 seconds