Chuk Kai Tai Chi, created by Sigong Chiu Chuk Kai, has its origins in China, was influenced by the Praying Mantis style and is very popular in Vietnam. Although based on a fighting style, it is characterised by slow movements, deep knee bends and emphasis on balance.
Here is a link to an excellent website in Vietnamese (http://www.thaicuchopnhat.org/) that describes the forms and lists the movements.
The most common form is Thái cực chưởng 132 thức (Chuk Kai Tai Chi 132 form) or Chiu Chuk Kai Taichi Mantis Cloudy Palms 132 forms.
The movements are:
1 Opening position
2 Holding hands
3 Turning arms to the left
4 Opening palms and lower body
5 Pushing palms
6 Holding tiger to return home
7 Pushing mountain and collapse columns
8 Leading dragon to the sea
9 Sweeping leaves with the wind
10 Raising hand and lift up body
12 Turning and stable the body
13 Calming external palms
14 Soothing peacock tails
15 One side whip
16 Rings flying obliquely
17 Turning to hold peacock tail
18 Opening neck palm
19 Rings flying obliquely
20 Lifting Yin palm 21 Sitting on horse to shoot arrow
22 Rings flying obliquely
23 Lifting Yin palm
24 Sitting on horse to shoot arrow
25 Phoenix facing the sun
26 Calming external palms
27 Upside down naughty monkey (3 times)
28 Right dividing horse hair
29 Left dividing horse hair
30 Scooping moon from the sea 31 Lifting arrow to shoot
32 Snake spitting poison
33 Rooster standing on one foot
34 Holding firmly to close
35 Holding tiger to return home
36 Opening neck palm
37 Step forward to thread pearls
38 Rings flying obliquely
39 Crane sucking in a sword
40 On side whip 41 Left soothing peacock tails
42 Right dividing horse hair
43 Stabilise in the centre
44 Chopping Hua Mountain with a single hand
45 Pointing the needle in the sea
46 Right dividing horse hair
47 Exploring sea with a needle
48 Pull arrow to shoot a tiger
49 Calming internal palms
50 Step forward to divide horse hair 51 Rings flying obliquely
52 Holding firmly to close
53 Lower position (right)
54 Cross hands
55 Stripping wings to kick
56 Right clouding hands
57 Left clouding hands
58 Step forward to divide horse hair
59 Rings flying obliquely
60 Holding firmly to close 61 Old man rowing a boat
62 Taking the sheep swiftly
63 Lifting foot (right)
64 Rings flying obliquely
65 Pushing the boat with water
66 Step forward to divide horse hair
67 Crane sucking in a sword
68 Turning to soothe peacock tails
69 Holding firmly to close
70 Horse returning to the stable 71 Smoothing moving Tai chi
72 Lower postures (left)
73 Turning to seal
74 Rooster standing on one foot
75 Crane sucking in a sword
76 Underarm needles
77 The beauty watching a mirror
78 Holding firmly to close
79 Horse returning to the stable
80 Facing a palm 81 Embracing a moon
82 Raising up high on a horse
83 Taking the sheep swiftly
84 Lifting foot (left)
85 Holding firmly to close
86 Ape presenting fruits (lift right foot)
87 Sitting on a horse to shoot arrow (right)
88 Crane sucking in a sword
89 Lifting Yin palm
90 Sitting on a horse to shoot arrow 91 Holding a Piba 1, Holding a Piba 2
92 Whipping a horse bottom to speed up
93 Lifting Yin palm
94 Sitting on a horse to shoot arrow
95 Spreading out cloud to hide the moon
96 Pushing in a new needle
97 Underarm needle
98 Holding a Piba
99 A lion opening its mouth
100 Lifting hands to raise up body 101 Turning body for underarm needle
102 Right clouding hands
103 Left clouding hands
104 Heavenly king to lift a pagoda
105 Holding a piba
106 Left dividing horsehair
107 Lifting yin palm
108 Pushing out fist
109 Chopping Hua Mountain with a single hand
110 Crossing dragon's hands 111 Raising up high on a horse
112 Kicking up feet
113 Left dividing horse hair
114 Pushing through a palm around waist
115 Holding firmly to close
116 Fisherman throwing out fish nets
117 Sitting on a horse to shoot arrow (right)
118 Ready to fight a tiger
119 Right dividing horse hair
120 Rings flying obliquely 121 Protecting palm internally
122 Soothing peacock tails
123 One side whip
124 Yin & yang palm
125 Holding firmly to close
126 Rings flying obliquely
127 Crane sucking in a sword
128 One side whip
129 Smart cat catching a mouse
130 Spreading cloud to see the moon
131 Golden child holding a seal
132 Closing posture
Master Van Liem Huynh performing the 132 form in Australia with English voice-over of the movements
The 132 form with movements in Vietnamese.
Master Cao Minh Tuyến performing the 132 form.
Master Cao Minh Tuyến performing the 132 form - rear view