Double jump is extremely important and must be used constantly.
Press the up arrow twice to double jump.
Use powerups wisely:
Use your powerups wisely as they'll be very useful to take out harder enemies quickly.
Conversely if your life line is very low use up your powerups to beat the level since if you die you lose all your powerups.
Keep number 1 gun charged:
Your default number 1 gun can pump out a few quick shots before it becomes drained and recharges slowly. Learn how to pump out quick shots and step away from battle to let it recharge.
Learn crouch attack:
Crouch and shoot to easily take out Grunt Soldiers and Grenade Droids.
Learn jump attack:
Jump about while firing to evade seeker rockets fired by Big Boys and Spider Mechs.
Taking out ceiling turrents:
Use triple shots to easily take out ceiling turrents, otherwise jump a lot to evade their shots.
Save your power-ups for difficult enemies. However, if you are low on health use power-ups to get you to the end of the level because they will be lost if you lose a life.
The default (number one) gun can shoot quickly a few times before it must be recharged.
Try shooting quickly, then retreat while it recharges.