Those enemies were a nightmare in the first XCOM and the situation hasn't changed much. Those units, thanks to their immense mobility, focus solely on melee combat - this way they can travel as must as a double the distance of a typical soldier while still being able to perform an attack.
Chryssalids deal good damage, they tend to score critical hits, they have considerable amount of health and a single point of armor, but the biggest threat comes from their abilities:
- Burrow. The mechanic perfectly known to all the Zerg lovers, a race from the Starcraft franchise, allowing them to hide underground and emerge from it when an unsuspecting prey comes into their range. This ability can be interrupted by using abilities, as well as items capable of scanning an area, which will force them above ground.
- Poison. Each attack of those aliens cause a special status effect on the target called "Chryssalid Poison". If the target dies while under the effect of the poison he / she will turn into a cocoon. If the cocoon is left for 3 rounds, 3 new Chryssalids will emerge from it.
In case that a cocoon appears on the battlefield, you must focus all of your remaining soldiers on it so that you prevent the enemy from gaining additional troops. Whenever you are moving through the area that you suspect a Chryssalid might be hiding, you should move with a single soldier only, while putting all the remaining units in Overwatch. By doing so you will eliminate all enemies that were hiding underground and decided to ambush your troops.
Note that Chryssalids almost always travel in groups, typically of 3 individuals - the only exception to this are the ones that are waiting underground, which are almost always found alone.