After completing story mode in Pokemon Ranger you will open up a new section:
Ranger Net.
Ranger Net will give you access to some new missions. Read on for some tips on the Deoxys mission.
Deoxys is able to change into multiple forms; normal, attack, speed and defense.
While on this mission you will have to defeat Deoxys in each of these forms. I highly recommend that you take the time to catch all three Machops that are available to you.
Why Machop? His Poke Assist power will cut the number of loops you need to make in half.
Attack Form Tips:
While in attack form Deoxys acts like a fighting type, he will attacks your stylus! After attacking your stylus he will become temporarily winded.
To capture him you need to fake him out by drawing a short line near the middle of the screen for him to attack. Do not let him hit it and as soon as his attack begins start to loop him.
Defense Form Tips:
Deoxys is very slow in defense form but you need a lot of loops to catch him. His one attack is also slow and sends out a black blob. He can also surround himself with a protective ball that will prevent your loops from counting.
To capture him is very easy. While he is preparing to generate the black blob begin looping him in a wide oval pattern. After the blob is released quickly shorten it to a tight circle. DO NOT hit the blob while doing this! If he goes into his protective ball keep looping, you will not lose the loops you have already made.
Speed Form Tips:
In speed form Deoxys is worse than Flygon. He zips all over the place and spends the majority of his time off the screen.
Your best bet is to use your Plusle/Minun and go for a paralyzation attack. He only takes 3 loops to catch.
Normal Form Tips:
Deoxys can only be "caught" while in normal form. Go for the paralyzation and nab him!
I hope these tips help!