Have most or all your buildings reach level 4.
On the town screen, watch your citizens wander around your city. Small thought bubbles will eventually appear above their heads. Click them to read their thoughts. The "Mind Reader" achievement requires one bubble to be read. The "Psion" achievement requires nine or ten bubbles to be read. The "Master Psion" achievement requires forty seven to fifty bubbles to be read.
Load level 1 (tutorial) and allow the Tutor to destroy your tower. Allow the game to idle until he is finished to avoid accidentally hitting him. This will require about one hour. You cannot use the "Surrender" option.
The "Strange Creatures" referenced are "Gelatinous Cubes" which are the blue cubes which hop along the path towards you. Kill 1000 of them to earn the achievement. Farm Tower 49 to encounter them frequently.
This achievement is based on the number of policy decisions related to "elementalist" made between missions. Once reaching about 70% elementalist the achievement will be earned.
Have 200,000 Triads in your account. You can accumulate that many Triads after completing the campaign and farming the harder levels while not spending much.
Turtooms are the turtle-like enemies that move towards your tower. Killing any type of them will increment the counter for this achievement. You must kill 10,000 Turtooms in the same city, but across any number of towers. Turtooms do not always appear on every tower. If you do not see one appear by the midpoint of the first wave, move to another level.