Well I'd rec demos if I could, but since UT is arsing me about, I can only do the next best thing - post the solutions as text. So here they are, now that I've finally figured this library PC out:
The Frigate Challenge
Spawn around the stairs, pick up the rocket-launcher and jump across to the armour.
Load your rockets as you are jumping to the armour and fire them at the turret outside as you dodge off the box (cluster fire).
Run outside along the wooden gangway and hammer-jump up onto the turret support.
Turn around 180 degrees and do a backwards hammer-jump up onto the top of the door surround on the top level.
From there, alt hammer-jump to the roof.
My record:
5:42 remaining
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The Bridge Challenge 1
Here goes...
Spawn in the high cave, grab the armour and load your hammer for a jump.
Backwards hammer-jump from the cave onto the torch nearest the Gate, then hammer-jump off this torch down to the lower level.
Dodge down to the beach then hammer-jump over the Main Gate (try to hammer-jump across the angle of the Gate, so that you land inside the minigun hut).
Grab the two health-packs and the thigh-pads, then dodge to the boots shed.
Jump onto the table to get the vials, then grab the boots.
Run round to the lift behind the sniper tower.
At this point there are two ways to get over the Gate again without wasting a jump. The first one is to use the lift behind the sniper tower, and that's the one I've timed for. The other one is to forward dodge up one of the sloped Gate supports, and alt-fire your hammer midway up the slope. However, this is so frustratingly difficult to get right first time that I just decided to forget it and allow the lift. Try the dodge way if you want though - you will still use the same number of boot jumps.
Jump off the lift with the boots, pressing forward and clicking alt-fire as you jump - you should land on the lower level underneath the bridge.
Jump from the lower level up onto the torch you landed on when you came out of the spawn cave.
You should have one boot jump remaining. Backwards hammer-jump from the torch towards the Final Assault Entrance, and hammer-jump again off the cliff to reach the bridge.
Grab the shock and dodge down to hit the Final Assault Entrance. This will trigger the Second Assault Entrance, which in turn will trigger the Main Gates.
You now have only the Explosives to get before the Detonator. Get all 4 as fast as possible, then backwards hammer-jump to the Detonator when you emerge from the far end of the Explosives area.
My record:
15:17 remaining
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The Bridge Challenge 2
Pick up the armour from the high cave, then get to the minigun hut as fast as possible.
Pick up the pads and health-packs, then get the boots and vials in the boots shed.
Backwards hammer-jump off the lift behind the minigun shed, and hammer-jump twice off the cliff face in midair to reach the bridge.
Run along the bridge towards the def spawn building. When you are underneath the highest window (the bit with the turret floor panel), jump with your boots and alt-fire your hammer off the bridge as you do so.
I used alt-fire because jumping with just the boots doesn't reach high enough, and doing a full boot / hammer-jump overshoots the window by miles.
Go through the Upper Base teleporter and dodge your merry way down to the Door Pressure Controller.
My record:
15:25 remaining
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The Bridge Challenge 3
Before I start, I'd just like to point out that there is a deliberate fundamental difference between the restrictions list for this challenge and the restrictions lists for the other 4. If you still can't work it out from this enormous, orange clue, read on and congratulate yourself for having the observational skills of a pair of trousers.
Apply godmode before the round starts (allowed within restrictions).
Start on the defending team
Pick up the rocket-launcher from the base and go through the Final teleporter.
Backwards hammer-jump off the bridge and land in the high cave where the attackers spawn.
Switch to the attacking team.
Launch yourself from the high cave to the bridge, using 6 clustered rockets from the rocket-launcher you just dropped.
Get the Explosives as fast as possible and backwards hammer-jump to the Detonator.
My record:
15:16 remaining
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I'll post demos as soon as I get the friggin thing working
I made two more challenges and I've posted them here:
http://forums.utassault.net/showthread.php?p=1204583#post1204583