Remember to circle the Kristallon and not just sit there, unless you want to just sit there and take damage or if you have the Diamond Formation.
Drag the Kristallon to the nearest portal or CBS to reduce damage from other aliens in the map—and other companies' hunters!
Only attack the Kristallons if you are dealing more than 2,000 damage (or with an Aegis), otherwise you will probably get nowhere.
Strangely enough, although you need to be level 11 to access the Kristallon's maps (X-6 and X-7) you can kill Boss Kristallons and even Uber Kristallons at level 10. This is because Boss Kristallons and Uber Kristallons reside in map 4-5 (Boss Kristallons are also found in X-7) which you only need to be level 10 to access while you need to be level 11 to be able to destroy regular Kristallons.
The Kristallon has the largest range of all the aliens requiring some extra effort when circling.
The Kristallon may sometimes change direction if you are circling it.