Does anyone know how to get an encounter with Cylero?

A few more details:

1. Because Cylero is further from the sun than Droo you need to start your transfer while Droo is "behind" Cylero in its orbit. Because the transfer orbit from Droo orbit to Cylero orbit has a shorter period than Cylero, you will "catch up" to Cylero.
2. Insanity is correct, the angle between Droo, the sun, and Cylero will need to be between 45 and 50 degrees. But FYI, this isn't magic, it is different depending on the two planets, and is proportional to the period of the transfer orbit and the angular velocity of the target body (here's the math).
3. When you make your burn to escape Droo you want to do it a few degrees after passing into the dark side of Droo. This is because when you make your orbit hyperbolic you want to exit Droo's orbit in the same direction it is traveling so that your excess velocity translates directly into raising the apoapsis of your transfer orbit around the sun.
4. The the greater the portion of the necessary Delta-V you put in while close to Droo the more efficient your transfer will be. If you wait until you have escaped Droo's SOI and then make another large burn to get your apoapsis up to Cylero's orbit you will waste >100 m/s.
5. Once you have left Droo's SOI you can tweak your arrival point and time by making a corrective burn, this burn will need to use a lateral component (the blue arrows) to shift your arrival time sooner or later, while correcting with a prograde/retrograde to keep your apoapsis lined up with Cylero's orbit.
6. Droo and Cylero both have 0 inclination so you shouldn't have to worry about that, but you should make sure your parking orbit around Droo before you start your transfer also has 0 inclination.

There are a few examples out there of crafts that calculate some of this for you, although I don't know of any that take eccentricity into account.