Well, once you finish Phalanx there's no pre-determined order to do the worlds.
1-2 is a major jump in difficulty from 1-1 though, you may want to do the X-1 worlds first, especially 2-1 and 4-1 (Leave 5-1 for when you have more skills, the 5-X worlds are hellishly difficult)
The trick in 1-2 is to either Kill the Dragon with a Bow (You'll need over 100 arrows for it, and you can aim easily and safely from the top of the first tower, where you get the Compound Long Bow), or to just rush the parts of the Dragon part, roll when you meet enemies, and face them inside the Towers themselves.
There are safe spots in which you can wait to the dragon passing by, you'll just need to watch closely to his sweeping pattern.
The Heater Shield is a nice addition to your arsenal, since it's the first 100% Physical Reduction shield you'll get in the game, and that makes tons of difference later on ;)
Current PC Build
CPU - i7 8700K 3.7 GHz (4.7 GHz turbo) 6 cores OC'd to 5.2 GHz with Watercooling (Hydro Series H110i) | MB - Gigabyte Z370 HD3P ATX | Gigabyte GTX 1080ti Gaming OC BLACK 11G (1657 MHz Boost Core / 11010 MHz Memory) | RAM - Corsair DIMM 32GB DDR4, 2400 MHz | PSU - Corsair CX650M (80+ Bronze) 650W | Audio - Asus Essence STX II 7.1 | Monitor - Samsung U28E590D 4K UHD, Freesync, 1 ms, 60 Hz, 28"
