To maximise your score you must hit as many targets consecutively without missing as you can. The first target is worth n x 1, the second n x 2 and so on. In stages with hundreds of potential targets one miss can drastically reduce your score.
The Scarecrow and Alternate Level Endings / Behaviour
Most levels have a scarecrow. If you hit the scarecrow 8 times and then shoot its head you will receive a 1000 point bonus and alter the behaviour of the level in some way.
For instance, in many (but not all) of the target levels hitting the first scarecrow in the first scene for the 1000 point bonus causes a second scarecrow to appear in the second scene. Hitting that scarecrow for a 1000 point bonus will result in an alternate third scene appearing. Generally it is possible to score more points in the alternate endings.
In other levels hitting the scarecrow for the 1000 point bonus results in less frantic movement from enemies (the red jumping crabs in the river, for instance).
Tip: zoom to hit the scarecrow.
Tip: hit the Red targets before the Yellow targets. This maximises your score as the yellow targets are worth more points.
Tip: zooming can be very effective.
Use the Grenade on Clustered Enemies
When facing flocks of birds or enemies that require multiple kills, the grenade is an effective way to rapidly increase your multiplier.
If you hold the trigger for 3 seconds you will fire a grenade when you release the trigger. Make sure you hit an enemy when pressing the trigger or you will reset your bonus multiplier.
This is effective against skeletons, flocks of bats and birds, and the flying lizards. It can even be used on clustered round targets, although it is usually quicker to shoot individual targets..