First, you need to find the Icarus Wings Bargain relic. This can be found anywhere you find relics and like other Bargains has a significant downside - you gain the ability to fly, but take double damage.
When you have this relic, go to the top of the Sun Tower to where you can enter the boss arena. The achievement should pop moving around near the entrance.
The difficulty of Sun Tower is largely around the outside platforming sections, but you can easily fly past all of them using the wings. Alternatively, if you see the wings earlier in a run but are worried about the double damage, get to the top of the Tower to unlock the portal and then go back for the wings so you can portal back with no risk.