Complete first and second parts
Use C2G57FLRDQJV7FBTCN as a password.
Getting the extra remote
Four remotes must be collected to complete a level. Since there are only three missions, only three remotes can be found. The fourth remote must be earned by collecting 100 flies in the level.
Training bonus
After completing training, you will get a bonus and another door will open in the Gex Cave.
Bonus Gex Cave items
There are four glass walls protecting items on the top level in the Gex Cave. Jump up and kick the glass to collect them. The timing on the jump is tricky, but you CAN break the glass by jumping and kicking.