Here is the MAP
I assume we start at f28

Up and Under
Go up over one log and below the next. Jump DC 10 to hop over the log (half movement speed), half movement as you go below.

At 50' speed and without running it takes 2 move actions to Arkom and 3 checks.
Jump1 DC10 (1d20+28)[35]
Jump2 DC10 (1d20+28)[48]
Jump3 DC10 (1d20+28)[42]
Starts at f28 stops at f13. End of round 1.


Low Wall
10 foot wall. DC 8 Jump and Climb DC 15 to pull yourself up and drop down the other side.

At 50' speed and without running it takes 1 move action to Arkom and 2 checks.
Jump DC8 (1d20+28)[44]
Climb DC15 (1d20+12)[15]
Stops at f6. Half of round 2.


High Wall
15 foot wall with rope. DC 5 Climb (one-quarter speed, one check per move action) up and down the other side.

At 50' speed and without running it takes 3 move actions to Arkom and 3 checks.
Climb 1 DC5 (1d20+12)[32]
Climb 2 DC5 (1d20+12)[14]
Climb 3 DC5 (1d20+12)[30]
Stops at f4. End of Round 3.


Step Logs
DC 10 Jump from one log to another. 8 jumps in total. Retry on each failure (for failed jump only, not from start).

At 50' speed and without running it takes 2 move actions to Arkom and 8 checks.
Jump1 DC10 (1d20+28)[32]
Jump2 DC10 (1d20+28)[39]
Jump3 DC10 (1d20+28)[29]
Jump4 DC10 (1d20+28)[47]
Jump5 DC10 (1d20+28)[47]
Jump6 DC10 (1d20+28)[33]
Jump7 DC10 (1d20+28)[41]
Jump8 DC10 (1d20+28)[34]
Stops at t1. End of round 4.


Rope Wall
30-foot rope wall climb up and down the other side. DC 10 Climb (one-quarter speed, one check per move action).

At 50' speed and without running it takes 5 move actions to Arkom and 5 checks.
Climb 1 DC10 (1d20+12)[27]
Climb 2 DC10 (1d20+12)[29]
Climb 3 DC10 (1d20+12)[31]
Climb 4 DC10 (1d20+12)[23]
Climb 5 DC10 (1d20+12)[26]
Stops at v1. Half of round 7.


Balance Logs
DC 15 Balance check (half speed). Retry on failure.

At 50' speed and without running it takes 2 move actions to Arkom and 2 checks.
Balance1 DC15 (1d20+11)[20]
Balance2 DC15 (1d20+11)[31]
Stops at I1. Half of round 8.


Monkey Bars
DC 20 Climb to brachiate across the monkey bars.

At 50' speed and without running it takes 1 move action to Arkom and 1 check.
Climb DC20 (1d20+12)[16]
Stops at S0. End of round 8.


Rope Bridge
One rope to walk on and another overhead to hold on. DC 20 Balance to cross (half speed).

At 50' speed and without running it takes 3 move actions to Arkom and 3 checks.
Balance1 DC20 (1d20+11)[20]
Balance2 DC20 (1d20+11)[26]
Balance3 DC20 (1d20+11)[12]
Stops at m1. Half of round 10.


Spider Climb
Traverse a wall sideways. DC 10 Climb (one-quarter speed, one check per move action).

At 50' speed and without running it takes 3 move actions to Arkom and 3 checks.
Climb 1 DC10 (1d20+12)[32]
Climb 2 DC10 (1d20+12)[19]
Climb 3 DC10 (1d20+12)[22]
Stops at q12. End of round 11.


Triple Jump
Running jump 3 times at increasing distances. DC 5, 10, and 15 Jump respectively. Retry on each failure (for failed jump only, not from start).

At 50' speed and without running it takes 2 move actions to Arkom and 3 checks.
Jump1 DC5 (1d20+28)[43]
Jump2 DC10 (1d20+28)[41]
Jump3 DC15 (1d20+28)[37]
Stops at p31. End of round 12.


Step Logs
DC 10 Jump from one log to another. 8 jumps in total. Retry on each failure (for failed jump only, not from start).

At 50' speed and without running it takes 2 move actions to Arkom and 8 checks.
Jump1 DC10 (1d20+28)[36]
Jump2 DC10 (1d20+28)[36]
Jump3 DC10 (1d20+28)[40]
Jump4 DC10 (1d20+28)[36]
Jump5 DC10 (1d20+28)[38]
Jump6 DC10 (1d20+28)[37]
Jump7 DC10 (1d20+28)[39]
Jump8 DC10 (1d20+28)[29]
Stops at e30. En of round 13.


Rope Swing
DC 14 Climb. Standard action to complete. Retry on failure.

It takes 1 standard action to Arkom and 1 checks.
Climb DC14 (1d20+12)[21]
Stops at Z30. Half of round 14.


Mudwalk
Cross 50 feet of waist-deep mud. Difficult terrain (half speed).

At 50' speed and without running it takes 3 move actions to Arkom.
Stops at I30 with 135feet. End of round 15.


Swim Lap
100-foot swim.

At 50' speed and without running it takes 4 full-round actions to Arkom and 4 checks.
Swim1 DC10 (1d20+17)[27]
Swim2 DC10 (1d20+17)[37]
Swim3 DC10 (1d20+17)[30]
Swim4 DC10 (1d20+17)[20]
Stops at o30. En of round 19.

And one more move action to reach i30 and finish. Half of round 20.

Extra rolls for use when retry is needed. To be used in order.
Spoiler
Show

1 (1d20)[5]
2 (1d20)[8]
3 (1d20)[19]
4 (1d20)[3]
5 (1d20)[18]
6 (1d20)[12]
7 (1d20)[12]
8 (1d20)[18]
9 (1d20)[15]
10 (1d20)[20]
11 (1d20)[12]
12 (1d20)[15]
13 (1d20)[20]
14 (1d20)[19]
15 (1d20)[4]
16 (1d20)[14]
17 (1d20)[12]
18 (1d20)[13]
19 (1d20)[2]
20 (1d20)[19]